Deck 8: Linear Programming Applications

Question 1

The constraints in a transportation problem deal with requirements at each origin and capacities at each destination.

Answer 1

False

Question 2

Production scheduling is amenable to solution by LP because it is a problem that must be solved on a regular basis.

Answer 2

True

Question 3

In a production scheduling problem, the inventory at the end of this month is set equal to the inventory at the end of last month + last month's production − sales this month.

Answer 3

False

Question 4

The linear programming approach to media selection problems is typically to either maximize the number of ads placed per week or to minimize advertising costs.

Question 5

If a linear programming problem has alternate solutions, the order in which you enter the constraints may affect the particular solution found.

Question 6

The linear programming model of the production mix problem only includes constraints of the less than or equal form.

Question 7

Since the production mix linear program applications are a special situation, the number of decision variables is limited to two.

Question 8

In the linear programming transportation model, the coefficients of the objective function can represent either the cost or the profit from shipping goods along a particular route.

Question 9

Linear programming variable names such as X₁₁, X₁₂, X₁₃, could possibly be used to represent production of a product (X_1j)over several months.

Question 10

A media selection LP application describes a method in which media producers select customers.

Question 11

The linear programming model of the production scheduling process can include the impact of hiring and layoffs, regular and overtime pay rates, and the desire to have a constant and stable production schedule over a several-month period.

Question 12

Transporting goods from several origins to several destinations efficiently is called the transportation problem.

Question 13

In general, linear programming is unable to solve complex labor planning as the objective function is usually not definable.

Question 14

In formulating the media selection linear programming model, we are unable to take into account the effectiveness of a particular presentation (e.g., the fact that only 5 percent of the people exposed to a radio ad will respond as desired).

Question 15

Another name for the transportation problem is the logistics problem.

Question 16

Determining the mixture of ingredients for a most economical feed or diet combination would be described as a production mix type of linear program.

Question 17

An ingredient or blending problem is a special case of the more general problem known as diet and feed mix problems.

Question 18

A marketing research linear programming model can help a researcher structure the least expensive, statistically meaningful sample.

Question 19

Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.

Question 20

The linear programming model of the production scheduling process is usually used when we have to schedule the production of multiple products, each of which requires a set of resources not required by the other products, over time.

Question 21

Which of the following is considered a decision variable in the media selection problem of minimizing interview costs in surveying?

A)the number of people to survey in each market segment
B)the overall survey budget
C)the total number surveyed
D)the number of people to conduct interviews

Question 22

Which of the following is considered a decision variable in the media selection problem of maximizing audience exposure?

A)the amount spent on each ad type
B)what types of ads to offer
C)the number of ads of each type
D)the overall advertising budget

Question 23

Which of the following does not represent a factor a manager might typically consider when employing linear programming for a production scheduling?

A)labor capacity
B)space limitations
C)product demand
D)risk assessment

Question 24

When linear programming is used to solve complex labor planning the objective function is usually the minimization of cost.

Question 25

The linear programming truck loading model always results in a practical solution.

Question 26

What is another name for blending problems?

A)diet problems
B)ingredient problems
C)feed mix problems
D)production mix problems

Question 27

The linear programming objective in a portfolio selection formulation is to maximize return.

Question 28

A linear programming approach is usually used by managers involved in portfolio selection to

A)maximize return on investment.
B)maximize investment limitations.
C)maximize risk.
D)minimize risk.

Question 29

The linear programming transportation model allows us to solve problems where supply does not equal demand.

Question 30

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as

A)the product mix problem.
B)the investment banker problem.
C)the Wall Street problem.
D)the portfolio selection problem.

Question 31

A typical constraint in the portfolio selection problem formulated in LP would be to maintain risk below some specified amount.

Question 32

In production scheduling LP problems, inventory at the end of this month is set equal to

A)inventory at the end of last month + this month's production - this month's sales.
B)inventory at the beginning of last month + this month's production - this month's sales.
C)inventory at the end of last month + last month's production - this month's sales.
D)inventory at the beginning of last month + last month's production - last month's sales.

Question 33

A linear programming approach is usually used by managers involved in portfolio selection to minimize risk.

Question 34

Media selection problems are typically approached with LP by either

A)maximizing audience exposure or maximizing number of ads per time period.
B)maximizing the number of different media or minimizing advertising costs.
C)minimizing the number of different media or minimizing advertising costs.
D)maximizing audience exposure or minimizing advertising costs.

Question 35

When formulating transportation LP problems, constraints usually deal with the

A)number of items to be transported.
B)distance goods are to be transported.
C)number of origins and destinations.
D)capacities of origins and requirements of destinations.

Question 36

Table 8-2
Diamond Jewelers is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv, newspaper, and radio.Information regarding cost and exposure is given in the table below:
Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads
According to Table 8-2, which describes a media selection problem, what would the objective function be?

A)Maximize 10T + 7N + 20R
B)Minimize 10T + 7N + 20R
C)Minimize 7000T + 8500N + 3000R
D)Maximize 7000T + 8500N + 3000R

Question 37

The linear programming ingredient or blending problem model allows one to include not only the cost of the resource, but also the differences in composition.

Question 38

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as the portfolio selection problem.

Question 39

Using linear programming to maximize audience exposure in an advertising campaign is an example of the type of linear programming application known as

A)media selection.
B)marketing research.
C)portfolio assessment.
D)media budgeting.

Question 40

Which of the following is considered a decision variable in the production mix problem of maximizing profit?

A)the amount of raw material to purchase for production
B)the number of product types to offer
C)the selling price of each product
D)the amount of each product to produce

Question 41

What will be the outcome of the linear program that uses the correct constraints but focuses on cost minimization rather than profit maximization?

A)The answer to this formulation will be identical to the profit maximization answer.
B)Each product will be produced to a level equal to its minimum constraint.
C)No raw materials will be used
D)The answer to this formulation will be identical to a revenue maximization formulation.

Question 42

Table 8-9

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $2 per yard, his zipper cost if $1 per foot, the dye is $1 per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. "In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. "We can make enough to get you out of the house now that I have 60,000 yards of leather, 50,000 feet of zipper material, 100,000 dye packets and 200,000 feet of thread."

One local distributer has placed an order for at least 5,000 purses and is willing to increase the order to a maximum of 10,000 if sales are strong. A purse requires 0.25 yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $41.50 for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $33.50 and jackets at $104. They want at least 10,000 jackets up to a ceiling of 15,000 and at least 10,000 pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires 1.5 yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least 2,500 backpacks but is unwilling to take more than 7,500. Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $22.50.


Use the information in Table 8-9 to formulate an LP approach to profit maximization.How many constraints (exclusive of the non-negativity constraint)should this problem have?

A)9
B)10
C)11
D)12

Question 43

The following problem type is such a special case of linear programming that a special algorithm has been developed to solve it.

A)the production mix problem
B)the diet problem
C)the ingredient mix problem
D)the transportation problem

Question 44

In the optimal solution to this scenario, purse production falls in between the upper and lower constraints.None of the items with maximum demands are produced to their limit.Which of these statements is valid?

A)The shadow price for purses must be zero.
B)Purses are more profitable than jackets.
C)It is more cost-effective to produce and sell leather pants than leather purses.
D)Nothing can be concluded from this statement.

Question 45

What is the objective in the diet problem?

A)maximize nutrition
B)minimize number of ingredients
C)minimize calories
D)minimize cost

Question 46

Table 8-9

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $2 per yard, his zipper cost if $1 per foot, the dye is $1 per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. "In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. "We can make enough to get you out of the house now that I have 60,000 yards of leather, 50,000 feet of zipper material, 100,000 dye packets and 200,000 feet of thread."

One local distributer has placed an order for at least 5,000 purses and is willing to increase the order to a maximum of 10,000 if sales are strong. A purse requires 0.25 yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $41.50 for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $33.50 and jackets at $104. They want at least 10,000 jackets up to a ceiling of 15,000 and at least 10,000 pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires 1.5 yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least 2,500 backpacks but is unwilling to take more than 7,500. Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $22.50.


Use the information in Table 8-9 to formulate an LP approach to profit maximization.How many decision variables should this problem have?

A)8
B)6
C)10
D)4

Question 47

Table 8-9

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $2 per yard, his zipper cost if $1 per foot, the dye is $1 per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. "In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. "We can make enough to get you out of the house now that I have 60,000 yards of leather, 50,000 feet of zipper material, 100,000 dye packets and 200,000 feet of thread."

One local distributer has placed an order for at least 5,000 purses and is willing to increase the order to a maximum of 10,000 if sales are strong. A purse requires 0.25 yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $41.50 for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $33.50 and jackets at $104. They want at least 10,000 jackets up to a ceiling of 15,000 and at least 10,000 pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires 1.5 yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least 2,500 backpacks but is unwilling to take more than 7,500. Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $22.50.


Use the information in Table 8-9 to answer this question.If Darrell elects to make 5000 purses, what is their total contribution to his profit?

A)$207,500
B)$190,000
C)$17,500
D)$225,000

Question 48

The shipping problem in LP is also called the

A)production mix problem.
B)freight train problem.
C)transportation problem.
D)land and sea problem.

Question 49

Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season.Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows.The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium.Given an advertising budget of $250,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem.

Question 50

A computer start-up named Pear is considering entering the U.S.market with what they believe to be a smaller and faster computer than some of the existing products on the market.They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product.They want to collect a reasonable sample from across the United States representative of all age brackets.They have split the United States into 2 regions: East and West.They want at least 65% of their sample to cover the East and no fewer than 25% of the West.They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up.They want at least 50% of their sample to be between 18 and 35 and at least 40% to be between 36 and 69.The costs per person surveyed is given in the table below:
Assume that at least 1,000 people are to be surveyed.The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements.Find the optimal solution and minimum cost.

Question 51

Which of the following statements is false regarding the portfolio selection problem?

A)The typical objective is to maximize the expected return on investment.
B)The constraints only pertain to risk.
C)Typical applications include banks, mutual funds, investment services, and insurance companies.
D)The problem typically includes both greater-than-or-equal-to and less-than-or-equal-to constraints.

Question 52

When applying linear programming to diet problems, the objective function is usually designed to

A)maximize ingredient blends.
B)minimize production losses.
C)maximize the number of products to be produced.
D)minimize the costs of nutrient blends.

Question 53

What is the objective in the truck loading problem?

A)minimize trucking distance
B)minimize the weight of the load shipped
C)maximize the value of the load shipped
D)minimize the cost of the load shipped

Question 54

Table 8-9

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $2 per yard, his zipper cost if $1 per foot, the dye is $1 per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. "In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. "We can make enough to get you out of the house now that I have 60,000 yards of leather, 50,000 feet of zipper material, 100,000 dye packets and 200,000 feet of thread."

One local distributer has placed an order for at least 5,000 purses and is willing to increase the order to a maximum of 10,000 if sales are strong. A purse requires 0.25 yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $41.50 for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $33.50 and jackets at $104. They want at least 10,000 jackets up to a ceiling of 15,000 and at least 10,000 pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires 1.5 yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least 2,500 backpacks but is unwilling to take more than 7,500. Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $22.50.


Use the information in Table 8-9 to formulate an objective function that strives for revenue maximization.

A)Maximize 41.50Pu + 33.50Pa + 22.50B + 104J
B)Maximize 38Pu + 24Pa + 17B + 92J
C)Maximize 3.5Pu + 9.5PsL + 5.5B + 12J
D)Maximize 2L + 1Z + 1D + 0.5T

Question 55

What are the decision variables in the diet problem?

A)amount of each ingredient to use
B)number of ingredients to use
C)amount of each type of food to purchase
D)number of items of food to purchase

Question 56

Which of the following statements is true regarding the labor planning problem?

A)It is typically a maximization problem.
B)Required labor hours translate into less-than-or-equal-to constraints.
C)The decision variables can include how many full- and part-time workers to use.
D)The problem is only unique to banks.

Question 57

When formulating transportation LP problems, the objective function usually deals with the

A)number of items to be transported.
B)choice of transportation mode (e.g., truck, airplane, railroad, etc.).
C)shipping cost or distances associated with transporting goods.
D)number of origins and destinations.

Question 58

Table 8-9

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $2 per yard, his zipper cost if $1 per foot, the dye is $1 per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. "In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. "We can make enough to get you out of the house now that I have 60,000 yards of leather, 50,000 feet of zipper material, 100,000 dye packets and 200,000 feet of thread."

One local distributer has placed an order for at least 5,000 purses and is willing to increase the order to a maximum of 10,000 if sales are strong. A purse requires 0.25 yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $41.50 for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $33.50 and jackets at $104. They want at least 10,000 jackets up to a ceiling of 15,000 and at least 10,000 pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires 1.5 yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least 2,500 backpacks but is unwilling to take more than 7,500. Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $22.50.


Use the information in Table 8-9 to formulate a constraint for the use of zipper material.

A)1Pu + 0.5Pa + 2B + 3J ≤ 50,000
B)3.5Pu + 9.5Pa + 5.5B + 12J ≤ 50,000
C)0.25L + 1Z + 1D + 2T ≤ 50,000
D)0.25Pu + 2Pa + 0.50B + 1.5J ≤ 50,000

Question 59

A computer start-up named Pear is considering entering the U.S.market with what they believe to be a smaller and faster computer than some of the existing products on the market.They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product.They want to collect a reasonable sample from across the United States representative of all age brackets.They have split the United States into 2 regions: East and West.They want at least 65% of their sample to cover the East and no fewer than 25% of the West.They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up.They want at least 50% of their sample to be between 18 and 35 and at least 40% to be between 36 and 69.The costs per person surveyed is given in the table below:
Assume that at least 1,000 people are to be surveyed.The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements.Formulate this problem as a linear program.

Question 60

A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection.Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection.Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection.The profit per table is $120, while the profit per chair is $80.Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time.To keep a balance, the number of chairs produced should be at least twice the number of tables.Also, the number of chairs cannot exceed six times the number of tables.Formulate this as a linear programming problem.Carefully define all decision variables.

Question 61

Green Acres just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1800 pounds of normal, the other for 3300 pounds of special.At least each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed.Green Grass has two input mixtures, A and B.Mixture A contains 80 percent perennial and 15 percent annual seed.Mixture B contains 70 percent annual and 25 percent perennial seed.Mixture A costs 85 cents per pound and mixture B costs 55 cents per pound.Set up the constraints and the objective function to solve this blending problem.
Let W = lbs.of mixture A used to produce the normal blend
X = lbs.of mixture A used to produce the special blend
Y = lbs.of mixture B used to produce the normal blend
Z = lbs.of mixture B used to produce the special blend

Question 62

Ivana Miracle wishes to invest up to her full inheritance of $300,000, and her goal is to minimize her risk subject to an expected annual return of at least $30,000.She has decided to invest her money in any of three possible ways-CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 15 percent; and a money market mutual fund, which is expected to return 8 percent.Risk factors are 1.0 for the CDs, 3.6 for the stocks, and 1.8 for the money market fund.What is the optimal solution and minimum risk value?

Question 63

A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection.Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection.Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection.The profit per table is $120, while the profit per chair is $80.Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time.To keep a balance, the number of chairs produced should be at least twice the number of tables.Also, the number of chairs cannot exceed six times the number of tables.How many tables and chairs should the furniture manufacturer produce to maximize profit?

Question 64

Dr.Barry Soprano wishes to invest his retirement fund of $2,200,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low.He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 5 percent; stocks that have an expected return of 22 percent; and a loan sharking business that is expected to return 58 percent.He has decided that the total $2,200,000 will be invested, but any part (or all)of it may be put in any of the three alternatives.Thus, he may have some money invested in all three alternatives.He has also decided to invest, at most, 50 percent of this in loansharking and at least 20 percent of this in CDs.Formulate this as a linear programming problem and solve in Excel.

Question 65

The following table provides shipping costs from each of two regional warehouses to each of three destinations.The supplies available and the demands are also given in the table.
Solve this conundrum in Excel.

Question 66

A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network.The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively.The models require the labor and materials per unit shown below.
How many of each model should be produced to maximize profit.What is the maximum profit?

Question 67

Green Acres just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1800 pounds of normal, the other for 3300 pounds of special.At least each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed.Green Grass has two input mixtures, A and B.Mixture A contains 80 percent perennial and 15 percent annual seed.Mixture B contains 70 percent annual and 25 percent perennial seed.Mixture A costs 85 cents per pound and mixture B costs 55 cents per pound.Solve this blending problem using Excel Solver.
Let W = lbs.of mixture A used to produce the normal blend
X = lbs.of mixture A used to produce the special blend
Y = lbs.of mixture B used to produce the normal blend
Z = lbs.of mixture B used to produce the special blend

Question 68

Three types of gasoline are manufactured by a company - Regular, Super, and Extra.Regular should have at least 11 percent additive 1 and 17 percent additive 2.Super should have at least 13 percent additive 1 and 22 percent additive 2.Extra should have at least 17 percent additive 1 and 19 percent additive 2.These are made by using two crudes - A and B.Crude A cost $28 per barrel and is 14 percent additive 1 and 18 percent additive 2.Crude B costs $30 per barrel and is 20 percent additive 1 and 24 percent additive 2.The demand for Regular is projected to be 1,000 barrels, while each of the others has a demand of 2,000 barrels.Formulate this as a linear programming problem to minimize cost while meeting all constraints.Carefully define all decision variables.

Question 69

A mail order firm, AmazingCo, can use one of 3 shipping couriers.Ajax Shipping charges $6 per pound and delivers in 2 days.Bilco Lanes charges $9 per pound but guarantees next day delivery.The final courier, Hobo Ltd., charges only $3 per pound but takes 4 days to deliver.AmazingCo has a quarterly budget of $280,000 and a reputation for timely delivery.Formulate the linear program so that the firm delivers as fast as possible within budget for 70,000 pounds of shipments per quarter.
Let X₁ = pounds using Ajax
X₂ = pounds using Bilco
X₃ = pounds using Hobo

Question 70

Foolish Manufacturing has three factories (1, 2, and 3)and three warehouses (A, B, and C).The table below shows the shipping costs between each factory (in dollars)and warehouse, the factory manufacturing capabilities (in 1000s), and the warehouse capacities (in 1000s).Solve this problem using Excel's Solver routine.

Question 71

A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network.The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively.The models require the labor and materials per unit shown below.
Formulate this product mix problem using linear programming.

Question 72

First Securities, Inc., an investment firm, has $380,000 on account.The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds.The following table shows the investment opportunities and rates of return.
The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock.Formulate this portfolio selection problem using linear programming.

Question 73

Ivana Miracle wishes to invest up to her full inheritance of $300,000, and her goal is to minimize her risk subject to an expected annual return of at least $30,000.She has decided to invest her money in any of three possible ways-CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 15 percent; and a money market mutual fund, which is expected to return 8 percent.Risk factors are 1.0 for the CDs, 3.6 for the stocks, and 1.8 for the money market fund.Formulate this as a linear program.

Question 74

A fast food restaurant uses full-time and part-time help to meet fluctuating demand during the day.The following table presents projected need for workers at different times of the day:
There is a maximum of four full-time workers and the other workers are part-time workers.Each full-time worker is there from 9:00 until 5:00, while the part-time workers will work for 4 consecutive hours at a cost of $4.00 per hour.The cost of the full-time worker is $50 per day.The company wishes to minimize total cost while meeting the demands.Formulate this as a linear programming problem.Carefully define all decision variables.

Question 75

Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs.Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection.Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection.Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection.The profit per table is $150 while the profit per chair is $100.Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time.To keep a balance, the number of chairs produced should be at least twice the number of tables.Also, the number of chairs cannot exceed 6 times the number of tables.Formulate this as a linear programming problem.Carefully define all decision variables.Find the solution.

Question 76

Foolish Manufacturing has three factories (1, 2, and 3)and three warehouses (A, B, andC).The table below shows the shipping costs between each factory (in dollars)and warehouse, the factory manufacturing capabilities (in 1000s), and the warehouse capacities (in 1000s).Write the objective function and the constraints.Let X_1A = 1000s of units shipped from factory 1 to warehouse A, etc.

Question 77

A cruise line is planning its menu for the next trip.Vacationers like eating steak, lobster, and chicken.The cruise line has decided to plan for at least half of all booked passengers to have a steak dinner, for at least a quarter of all passengers to have lobster, and the rest to have chicken.Steak dinners cost the company $8, lobsters cost $15, and chicken costs the line $4.On the next cruise, there are 400 passengers booked.In addition, the cruise line has decided to plan for an additional 25% more meals than bookings.Formulate the appropriate linear program.
Let X₁ = steak meals
X₂ = lobster meals
X₃ = chicken meals

Question 78

The following table provides shipping costs from each of two regional warehouses to each of three destinations.The supplies available and the demands are also given in the table.
Formulate this as a linear programming problem.Carefully define all decision variables.

Question 79

Dr.Randy Heizer wishes to invest his retirement fund of $2,200,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low.He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 5 percent; stocks that have an expected return of 22 percent; and a loan sharking business that is expected to return 58 percent.He has decided that the total $2,200,000 will be invested, but any part (or all)of it may be put in any of the three alternatives.Thus, he may have some money invested in all three alternatives.He has also decided to invest, at most, 50 percent of this in loansharking and at least 20 percent of this in CDs.Formulate this as a linear programming problem and carefully define all the decision variables.

Question 80

Three types of fertilizer are manufactured by a company: Regular, Supergro, and Jungle Feeder.Regular should have at least 10 percent nitrogen and 16 percent phosphorous.Supergro should have at least 12 percent nitrogen and 20 percent phosphorous, and Jungle Feeder should have at least 15 percent nitrogen and 18 percent phosphorous.These are made by using two components: A and B.Component A costs $0.30 per pound and is 14 percent nitrogen and 18 percent phosphorous.Component B costs $0.50 per pound and is 20 percent nitrogen and 24 percent phosphorous.The demand for Regular is projected to be 1,000 pounds, while each of the others has a demand of 2,000 pounds.Formulate the appropriate linear program.
Let X₁ = pounds of component A in Regular
X₂ = pounds of component A in Supergro
X₃ = pounds of component A in Jungle Feeder
X₄ = pounds of component B in Regular
X₅ = pounds of component B in Supergro
X₆ = pounds of component B in Jungle Feeder