950 CHAPTER 9 Systems and Matrices 84. Shipping Requirements The California Almond Growers have 2400 boxes of almonds to be shipped from their plant in Sacramento to Des Moines and San Antonio. The Des Moines market needs at least 1000 boxes, while the San Antonio market must have at least 800 boxes. Solve each problem. See Examples 4 and 5. 85. Aid to Disaster Victims An agency wants to ship food and clothing to tsunami victims in Japan. Commercial carriers have volunteered to transport the packages. Each 20-ft3 box of food weighs 40 lb and each 30-ft3 box of clothing weighs 10 lb. The total weight cannot exceed 16,000 lb, and the total volume must be at most 18,000 ft3. Each carton of food will aid 10 people, and each carton of clothing will help 8 people. How many cartons of food and clothing should be sent to maximize the number of people assisted? What is the maximum number assisted? 86. Aid to Disaster Victims Refer to Example 4. Suppose that each medical kit aids 2 people rather than 6, and each container of water serves 5 people rather than 10. How many of each should be sent in order to maximize the number of people assisted? What is this maximum number assisted? 87. Storage Capacity An office manager wants to buy some filing cabinets. Cabinet A costs $10 each, requires 6 ft2 of floor space, and holds 8 ft3 of files. Cabinet B costs $20 each, requires 8 ft2 of floor space, and holds 12 ft3 of files. He can spend no more than $140, and there is room for no more than 72 ft2 of cabinets. To maximize storage capacity within the limits imposed by funds and space, how many of each type of cabinet should he buy? What is the maximum storage capacity? 88. Gasoline Revenues A manufacturing process requires that oil refineries manufacture at least 2 gal of gasoline for each gallon of fuel oil. To meet the winter demand for fuel oil, at least 3 million gal per day must be produced. The demand for gasoline is no more than 6.4 million gal per day. If the price of gasoline is $2.90 per gal and the price of fuel oil is $2.50 per gal, how much of each should be produced to maximize revenue? What is the maximum revenue? 89. Diet Requirements Theo requires two food supplements, I and II. He can get these supplements from two different products, A and B, as shown in the table. He must include at least 15 g of each supplement in his daily diet. If product A costs $0.25 per serving and product B costs $0.40 per serving, how many servings of each should he take daily to minimize cost? What is the minimum cost? Supplement (g/serving) I II Product A 3 2 Product B 2 4 90. Profit from Televisions The GL company makes televisions. It produces a 32-inch model that sells for $100 profit and a 48-inch model that sells for $150 profit. On the assembly line, the 32-inch model requires 3 hr, and the 48-inch model takes 5 hr. The finishing shop spends 1 hr on the finishes for the 32-inch model and 3 hr on the finishes for the 48-inch model. Both models require 2 hr of time for testing and packing. On one production run, the company has available 3900 work hours on the assembly line, 2100 work hours on the finishing line, and 2200 work hours in the testing and packing department. How many of each model should it produce to maximize profit? What is the maximum profit?
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