Exam 8: Linear Programming Applications

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

Media selection problems are typically approached with LP by either

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

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.

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?

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.

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.

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?

What is the objective in the truck loading problem?

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

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

Describe a diet problem linear programming application.

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.

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.

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.

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

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

Describe the shipping problem linear programming application.

Describe the truck loading linear programming application.

Describe the production scheduling linear programming application.