Assignment

Q-1: The marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine ads to run during the next quarter. Each TV spot costs $5,000 and is expected to increase sales by 300,000 cans. Each magazine ad costs $2,000 and is expected to increase sales by 500,000 cans. Atotal of $100,000 may be spent on TV and magazine ads; however, Mountain Mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads. Mountain Mist earns a profit of $0.05 on each can it sells. Formulate an LP model for this problem.

Q-2: Blacktop Refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore type 1 contains 20% copper, 20% zinc and 15% magnesium. Each ton of ore type 2 contains 30% copper, 25% zinc and 10% magnesium. Ore type1 cost $90 per ton and ore type 2 costs $120 per ton. Blacktop would like to buyenough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesiumin the least costly manner. Formulate an LP model for this problem.

Q-3: The Electrotech Corporation manufactures two industrial-sized electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for a $250 profit. Each alternator requires 3 hours of wiring and 2 hours of testing and can be sold for a $150 profit. There are 260 hours of wiring time and 140 hours of testing time available in the next production period and Electrotech wants to maximize profit. Formulate an LP model for this problem.

Q-4: Refer to the previous question. Suppose that Electrotech's management decides thatthey need to make at least 20 generators and at least 20 alternators. Reformulate your LP model to account for this change.

Q-5: Bill's Grill is a popular college restaurant that is famous for its hamburgers. The owner of the restaurant, Bill, mixes fresh ground beef and pork with a secret ingredient to make delicious quarter-pound hamburgers that are advertised as having no more than 25% fat. Bill can buy beef containing 80% meat and 20% fat at $0.85 per pound. He can buy pork containing 70% meat and 30% fat at $0.65 per pound. Bill wants to determine the minimum cost way to blend the beef and pork to make hamburgers that have no more than 25% fat. Formulate an LP model for this problem.

Q-6: Zippy motorcycle manufacturing produces two popular pocket bikes (miniaturemotorcycles with 49cc engines): the Razor and the Zoomer. In the coming week, the manufacturer wants to produce a total of up to 700 bikes and wants to ensure that the number of Razors produced does not exceed the number of Zoomers by more than 300. Each Razor produced and sold results in a profit of $70, and each Zoomerresults in a profit of $40. The bikes are identical mechanically and differ only in the appearance of the polymer-based trim around the fuel tank and seat. Each Razor's trim requires 2 pounds of polymer and 3 hours of production time, and each Zoomerrequires 1 pound of polymer and 4 hours of production time. Assume that 900 pounds of polymer and 2400 labor hours are available for production of these items in the coming week. Formulate an LP model for this problem.

Q-7: A farmer in Georgia has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 2.5 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about $3 each, and cantaloupes will sell for about $1 each. Every acre planted with watermelons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of $10 per 50-pound bag. Finally, the farmer can hire laborers to harvest the fields at a rate of $5 per hour. If the farmer sells all the watermelons and cantaloupes he produces, how many acres of each crop should the farmer plant to maximize profits? Formulate an LP model for this problem.

Q-8: Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through 3 manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes insanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting,45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours offinishing capacity. Assume that all doors produced can be sold for a profit of $500and all windows can be sold for a profit of $400. Formulate an LP model for this problem.

Q-9:PC-Express is a computer retail store that sells two kinds of microcomputers: desktopsand laptops. The company earns $600 on each desktop computer it sells and$900 on each laptop. The microcomputers PC-Express sells are manufactured byanother company. This manufacturer has a special order to fill for another customerand cannot ship more than 80 desktop computers and 75 laptops to PC-Express nextmonth. The employees at PC-Express must spend about 2 hours installing softwareand checking each desktop computer they sell. They spend roughly 3 hours to completethis process for laptop computers. They expect to have about 300 hours availablefor this purpose during the next month. The store's management is fairly certain that they can sell all the computers they order, but are unsure how manydesktops and laptops they should order to maximize profits.Formulate an LP model for this problem.

Q-10: American Auto is evaluating their marketing plan for the sedans, SUVs, and trucks they produce. A TV ad featuring this SUV has been developed. The company estimates that each showing of this commercial will cost $500,000 and increase sales of SUVs by 3%, but reduce sales of trucks by 1%, and have no effect of the sales of sedans. The company also has a print ad campaign developed that it can run in various nationally distributed magazines at a cost of $750,000 per title. It is estimated that each magazine title the ad runs in will increase the sales of sedans, SUVs, and trucks by 2%, 1%, and 4%, respectively. The company desires to increase sales of sedans, SUVs, and trucks by at least 3%, 14%, and 4%, respectively, in the least costly manner. Formulate an LP model for this problem.

Q-11:A furniture manufacturer produces two types of tables (country and contemporary) using three types of machines. The time required to produce the tables on each machine is given in the following table.

Country tables sell for $350 and contemporary tables sell for $450. Management has determined that at least 20% of the tables made should be country and at least 30% should be contemporary. How many of each type of table should the company produce if it wants to maximize its revenue? Formulate an LP model for this problem.

Q-12: Tarmac Chemical Corporation produces a special chemical compound-calledCHEMIX-that is used extensively in high school chemistry classes. This compound must contain at least 20% sulfur, at least 30% iron oxide, and at least 30% but no more than 45% potassium. Tarmac's marketing department has estimated that it will need at least 600 pounds of this compound to meet the expected demand during the coming school session. Tarmac can buy three compounds to mix together to produce CHEMIX. The makeup of these compounds is shown in the following table.

Compounds 1, 2, and 3 cost $5.00, $5.25, and $5.50 per pound, respectively. Tarmac wants to use an LP model to determine the least costly way of producing enough CHEMIX to meet the demand expected for the coming year. Formulate an LP model for this problem.

Q-13: Maintenance at a major theme park in central Florida is an ongoing process that occurs 24 hours a day. Because it is a long drive from most residential areas to the park, employees do not like to work shifts of fewer than eight hours. These 8-hour shifts start every four hours throughout the day. The number of maintenance workers needed at different times throughout the day varies. The following table summarizes the minimum number of employees needed in each 4-hour time period.

The maintenance supervisor wants to determine the minimum number of employees to schedule that meets the minimum staffing requirements. Formulate an LP model for this problem.