A manufacturer of skis produces two types: telemark and cross country. It takes the manufacturer 4 hours to produce each pair of telemark skis and 2

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1 A manufacturer of skis produces two types: telemark and cross country. It takes the manufacturer 4 hours to produce each pair of telemark skis and 2 hours to produce each pair of cross country skis. The maximum time available for production each week is 80 hours. It takes 2 hours to wax and put finishing touches on each pair of telemark skis and it takes 2 hours to complete the same processes for the cross country skis. The maximum time allowed for waxing and finishing altogether is 64 hours each week. When the skis are sold the manufacturer makes $140 profit on the telemark skis and $100 profit on the cross country skis. How many skis of each type must be produced each week to achieve a maximum profit?

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3 A Linear Programming Application: Radio Shack Beaters You are the assistant manager of an appliance store. The manager has asked you to do a cost analysis to figure out what stereo systems the store should order. Next month you will order two types of stereo systems, a less expensive Model A and a more expensive Model B. As assistant manager you must figure out how much of each model to order to minimize costs. You expect to sell at least 100 units some Model A and some Model B. Model A leaves a $40 profit for the store. Model B leaves a $60 dollar profit for the store. Total profits must be at least $4800. The wholesale cost of Model A is $250 dollars. The wholesale cost of model B is $400. As a store you by at the wholesale cost. What does a point in the solution region represent? How does it compare to a point not in your solution region? ind the minimum and maximum costs (if they exist). ow many of each model should you order to minimize your costs? What is the profit when all items are sold? fter reviewing your report, the manager decides that the store must order at least 30 Model B stereos even if it increases the inimum cost. You go back to the drawing board to revise your analysis. Now how many of each model should be ordered to minimize costs? What is the profit when all items are sold?

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5 A calculator company produces a scientific calculator and a graphing calculator. Long term projections indicate an expecte demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

6 You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize shorage volume?

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11 In order to ensure optimal health (and thus accurate test results), a lab technician needs to the rabbits a daily diet containi a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protien. But the rabbits should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Fo Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend?

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13 A building supply has two locations in town. The office receives orders from two customers, each requiring 3/4 inch plywoo Customer A needs fifty sheets and Customer B needs seventy sheets. The warehouse on the east side of town has eighty sheets in stock; the west side warehouse has forty five sheets in stock. Delivery costs per sheet are as follows: $0.50 from the eastern warehouse to Customer A, $0.60 from the eastern warehouse Customer B, $0.40 from the western warehouse to Customer A, and $0.55 from the western warehouse to Customer B. Find the shipping arrangement which minimizes costs.

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