## Spreadsheet Modeling and Decision Analysis Study Set 2

Statistics

## Quiz 2 :

Introduction to Optimization and Linear Programming

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Q24 Q24 Q24

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X

_{1}= number of product 1 produced in each batch X_{2}= number of product 2 produced in each batch How much profit is earned per each unit of product 2 produced?Free

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Multiple Choice

Q25 Q25 Q25

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X

_{1}= number of product 1 produced in each batch X_{2}= number of product 2 produced in each batch How many units of resource 1 are consumed by each unit of product 1 produced?Free

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Multiple Choice

Q26 Q26 Q26

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X

_{1}= number of product 1 produced in each batch X_{2}= number of product 2 produced in each batch How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?Free

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Multiple Choice

Q27 Q27 Q27

A company uses 4 pounds of resource 1 to make each unit of X

_{1}and 3 pounds of resource 1 to make each unit of X_{2}. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X_{1}, X_{2}and resource 1?Free

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Multiple Choice

Q28 Q28 Q28

A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C?

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Multiple Choice

Q56 Q56 Q56

The Happy Pet pet food company produces dog and cat food. Each food is comprised of meat, soybeans and fillers. The company earns a profit on each product but there is a limited demand for them. The pounds of ingredients required and available, profits and demand are summarized in the following table. The company wants to plan their product mix, in terms of the number of bags produced, in order to maximize profit.
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.

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Q57 Q57 Q57

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.
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.

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Q58 Q58 Q58

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 a limited demand. There are a limited number of wiring, assembly and inspection hours available next month. The data for this problem is summarized in the following table.
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.

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Q59 Q59 Q59

The Big Bang explosives company produces customized blasting compounds for use in the mining industry. The two ingredients for these explosives are agent A and agent B. Big Bang just received an order for 1400 pounds of explosive. Agent A costs $5 per pound and agent B costs $6 per pound. The customer's mixture must contain at least 20% agent A and at least 50% agent B. The company wants to provide the least expensive mixture which will satisfy the customers requirements.
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.

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Q60 Q60 Q60

Jim's winery blends fine wines for local restaurants. One of his customers has requested a special blend of two burgundy wines, call them A and B. The customer wants 500 gallons of wine and it must contain at least 100 gallons of A and be at least 45% B. The customer also specified that the wine have an alcohol content of at least 12%. Wine A contains 14% alcohol while wine B contains 10%. The blend is sold for $10 per gallon. Wine A costs $4 per gallon and B costs $3 per gallon. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.
c.
How much profit will Jim make on the order?

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Q61 Q61 Q61

Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are:
Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.
Formulate the LP model for this problem.

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Q62 Q62 Q62

Project 2.1
Joey Koons runs a small custom computer parts company. As a sideline he offers customized and pre-built computer system packages. In preparation for the upcoming school year, he has decided to offer two custom computer packages tailored for what he believes are current student needs. System A provides a strong computing capability at a reasonable cost while System B provides a much more powerful computing capability, but at a higher cost. Joey has a fairly robust parts inventory but is concerned about his stock of those components that are common to each proposed system. A portion of his inventory, the item cost, and inventory level is provided in the table below.
The requirements for each system are provided in the following table:
Each system requires assembly, testing and packaging. The requirements per system built and resources available are summarized in the table below.
Joey is uncertain about product demand. In the past he has put together similar types of computer packages but his sales results vary. As a result is unwilling to commit all his in-house labor force to building the computer packages. He is confident he can sell all he can build and is not overly concerned with lost sales due to stock-outs. Based on his market survey, he has completed his advertising flyer and will offer System A for $ 1250 and will offer system B for $ 2325. Joey now needs to let his workers know how many of each system to build and he wants that mix to maximize his profits.
Formulate an LP for Dave's problem. Solve the model using the graphical method. What is Dave's preferred product mix? What profit does Dave expect to make from this product mix?

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