## Spreadsheet Modeling and Decision Analysis Study Set 2

Statistics

## Quiz 3 :

Modeling and Solving Lp Problems in a Spreadsheet

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Q30 Q30 Q30

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is
-Refer to Exhibit 3.1. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?

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Q31 Q31 Q31

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is
-Refer to Exhibit 3.1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?

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Q32 Q32 Q32

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is
-Refer to Exhibit 3.1. Which cells should be changing cells in this problem?

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Q33 Q33 Q33

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is
-Refer to Exhibit 3.1. Which cells should be the constraint cells in this problem?

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Q34 Q34 Q34

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is
-Refer to Exhibit 3.1. Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?

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Q35 Q35 Q35

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows.
The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
-Refer to Exhibit 3.2. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?

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Q36 Q36 Q36

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows.
The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
-Refer to Exhibit 3.2. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of wiring used?

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Q37 Q37 Q37

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows.
The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
-Refer to Exhibit 3.2. Which cells should be changing cells in this problem?

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Q38 Q38 Q38

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows.
The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
-Refer to Exhibit 3.2. Which cells should be the constraint cells in this problem?

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Q39 Q39 Q39

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows.
The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
-Refer to Exhibit 3.2. Which of the following statements will represent the constraint for just assembly hours?

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Q40 Q40 Q40

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows.
Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
-Refer to Exhibit 3.3. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total cost?

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Q41 Q41 Q41

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows.
Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
-Refer to Exhibit 3.3. What formula should be entered in cell D11 in the accompanying Excel spreadsheet to compute the total liters of alcohol supplied?

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Q42 Q42 Q42

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows.
Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
-Refer to Exhibit 3.3. Which cells should be changing cells in this problem?

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Q43 Q43 Q43

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows.
Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
-Refer to Exhibit 3.3. Which cells should be the constraint cells in this problem?

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Q44 Q44 Q44

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows.
Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
-Refer to Exhibit 3.3. Which of the following statements could represent a constraint in this problem?

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Q45 Q45 Q45

Exhibit 3.4
The following questions are based on this problem and accompanying Excel windows.
A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
-Refer to Exhibit 3.4. What formula should be entered in cell B7 in the accompanying Excel spreadsheet to compute total dollars invested?

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Q46 Q46 Q46

Exhibit 3.4
The following questions are based on this problem and accompanying Excel windows.
A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
-Refer to Exhibit 3.4. What formula should be entered in cell D7 in the accompanying Excel spreadsheet to compute the total return?

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Q47 Q47 Q47

Exhibit 3.4
The following questions are based on this problem and accompanying Excel windows.
A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
-Refer to Exhibit 3.4. Which cells are changing cells in the accompanying Excel spreadsheet?

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Q48 Q48 Q48

Exhibit 3.5
The following questions are based on this problem and accompanying Excel windows.
A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
-Refer to Exhibit 3.5. What formula should be entered in cell C6 in the accompanying Excel spreadsheet to compute ending inventory?

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Q49 Q49 Q49

Exhibit 3.5
The following questions are based on this problem and accompanying Excel windows.
A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
-Refer to Exhibit 3.5. What formula should be entered in cell C18 in the accompanying Excel spreadsheet to compute the quarterly carrying costs?

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Q50 Q50 Q50

Exhibit 3.5
The following questions are based on this problem and accompanying Excel windows.
A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
-Refer to Exhibit 3.5. Which cells are changing cells in the accompanying Excel spreadsheet?

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Q51 Q51 Q51

Exhibit 3.5
The following questions are based on this problem and accompanying Excel windows.
A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
-Refer to Exhibit 3.5. What formula could be entered in cell F20 in the accompanying Excel spreadsheet to compute the Total Cost for all four quarters?

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Q61 Q61 Q61

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem.
Formulate the LP for this problem.

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Q62 Q62 Q62

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem.
Enter the numbers in the appropriate cells of ranges B12:D12 and E8:F12 in the Excel spreadsheet to solve this problem based on the following formulation.

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Q63 Q63 Q63

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem.
What are the key formulas for this Excel spreadsheet implementation of the following formulation?

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Q64 Q64 Q64

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
Formulate the LP for this problem.

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Q65 Q65 Q65

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
Enter the numbers in the appropriate cells of ranges B6:G11 and B13:G13 in the Excel spreadsheet to solve this problem based on the following formulation.

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Q66 Q66 Q66

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
What are the key formulas for this Excel spreadsheet implementation of the following formulation?

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Q67 Q67 Q67

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of the formulation for this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

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Q68 Q68 Q68

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
Formulate the LP for this problem.

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Q69 Q69 Q69

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
Enter the numbers in the appropriate cells of range B5:F10 in the Excel spreadsheet to solve this problem based on the following formulation.

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Q70 Q70 Q70

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
What are the key formulas for this Excel spreadsheet implementation of the following formulation?

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Q71 Q71 Q71

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of the formulation for this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

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Q72 Q72 Q72

State Farm Supply has just received an order for 10,000 pounds of chicken feed. The farmer has specified certain that the feed meet minimum requirements for Protein, Carbohydrate, Fat and Vitamins. State Farm can blend four different feeds to produce the required mix. The farmer would like to pay the lowest possible price for the feed. The data for the problem is summarized in the following table.
Formulate the LP for this problem.

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Q73 Q73 Q73

A paper mill has received an order for rolls of paper. The customer wants 400 12" wide rolls, 300 18" rolls and 200 24" rolls. The company has 40" wide rolls of paper which it can slit to the appropriate width. The company wants to minimize the number of rolls it must use to fill the order.
Formulate the LP for this problem.

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Q74 Q74 Q74

Pete's Plastics manufactures plastic at plants in Miami, St. Louis and Cleveland. Pete needs to ship plastic to customers in Pittsburgh, Atlanta and Chicago. He wants to minimize the cost of shipping the plastic from his plants to his customers. The data for the problem is summarized in the following table.
Formulate the LP for this problem.

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Q75 Q75 Q75

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
Formulate the LP for this problem.

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Q76 Q76 Q76

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

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Q77 Q77 Q77

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
What formulas are required for the following cells in the Excel spreadsheet implementation of the formulation?
B7
D7
F7
H7

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Q78 Q78 Q78

A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost, demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 100 units and management wants to keep at least 50 units on hand. Quarterly inventory holding cost is 4% of the cost of production. There are currently 50 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
What formulas are required for cells D3, D6, D8, D15, D17 and D18 in the Excel spreadsheet implementation of the formulation?

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Q79 Q79 Q79

A grain store has six types of grain, each varying in cost, quality, and nutritional content. Periodically, excess inventory of these grains are consolidated into two local products, Feed-M-All and Supreme-Feed. Feed-M-All sells for $6.50 for a 10-pound bag while Supreme-Feed sells for $8.50 for a 10-pound bag. These feeds are advertised as having the following nutritional content:
The component grains have the following content characteristics:
Targets for Feed-M-All are a cost of $ 4.35 per 10-pound bag, a quality rating of 2.25, along with the minimum percentages of protein and fat, and the maximum percentage of carbohydrates. Similar targets are set for Supreme-Feed with cost set at $ 4.60 and quality at 2.45. There must be at least a 70%-30% mix among these two local feeds.
Formulate an LP model for this product mix problem.

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Q80 Q80 Q80

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
Formulate an LP model for this logistics problem.

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Q81 Q81 Q81

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
The following is the LP model for this logistics problem.
What formula goes in cells F10, E3, E4, E5, and B6 of this Excel spreadsheet?

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Q82 Q82 Q82

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
The following is the LP model for this logistics problem.
What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

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Q83 Q83 Q83

Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations:
Formulate an LP model for Robert to maximize his numerical grade.

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Q84 Q84 Q84

Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations:
The following LP model allows Robert to maximize his numerical grade.
What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

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The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months.
Based on the following formulation, is City East efficient? If not, what input and output values should they aspire to in order to become efficient?

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Q86 Q86 Q86

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months.
Enter the numbers in the appropriate cells of ranges B4:H6 in the Excel spreadsheet to solve this problem based on the following formulation.

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Q87 Q87 Q87

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months.
What are the key formulas for this Excel spreadsheet implementation of the following formulation?

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Q88 Q88 Q88

Project 3.1 The Diet Problem: Ordering Meals from McDonald's
Based on: Robert A. Bosch, "Big Mac Attack: The Diet Problem revisited, Eating at McDonald's," OR/MS Today, August 1993, pp 30-31.
Tina Simpson is a new fourth-grade teacher at Forest Ridge Elementary. The first teacher workshop for the upcoming school year is next Monday and by majority vote, McDonald's was selected as the food of choice. As the new person, Tina is tasked with developing the meal for the workshop. McDonald's has graciously offered to deliver whatever food Tina decides to order, along with a variety of condiments applicable to whatever is ordered. Rather than offer a menu choice, Tina has decided to simply order the same meal for each person in the workshop.
To get started, Tina took a trip to McDonald's and obtained their published information on the nutritional content of their food. That data is summarized in the table below.
Tina wants the meal to be nutritionally complete. The National Research Council publishes their Recommended Daily Allowances. In this publication, they contend that a diet (in this case the meal) should provide at least 100 percent of the U.S. RDA of numerous nutrients. The specific amount of the RDA depends on such factors as age, weight and gender. In addition, the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol. Further, at most 30 percent of the calories consumed should come from fat, and at most 10 percent from saturated fat. Each gram of fat contains 9 calories.
Based on the above information, Tina wants to design a least-cost meal that provides at least 100% of the U.S. RDA of vitamins A, C, B

_{1}, B_{2}, niacin, calcium, and iron; supplies at least 55 grams of protein; contains at most 3 grams of sodium; and contains at most 30 percent of its calories from fat. Only those foods list in the table above are available for the meal. Formulate the LP model for Tina's problem. Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements. What is the recommended meal? Is this meal reasonable? If not, modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.Free

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