987 CHAPTER 9 Review Exercises Solve each problem. 69. Cost of Nutrients Certain laboratory animals must have at least 30 g of protein and at least 20 g of fat per feeding period. These nutrients come from food A, which costs $0.18 per unit and supplies 2 g of protein and 4 g of fat; and from food B, which costs $0.12 per unit and has 6 g of protein and 2 g of fat. Food B is purchased under a long-term contract requiring that at least 2 units of B be used per serving. How much of each food must be purchased to produce the minimum cost per serving? What is the minimum cost? 70. Profit from Farm Animals A 4-H member raises only geese and pigs. She wants to raise no more than 16 animals, including no more than 10 geese. She spends $5 to raise a goose and $15 to raise a pig, and she has $180 available for this project. Each goose produces $6 in profit, and each pig produces $20 in profit. How many of each animal should she raise to maximize her profit? What is her maximum profit? Find the values of the variables for which each statement is true, if possible. 71. c 5 -6y x + 2 z d = c a 5y 3x - 1 9 d 72. c -6 + k -2 + m 2 3p a + 3 2r d + c 3 - 2k 5 5 8p 7 5rd = c 5 2m y 11 6a -35d Perform each operation, if possible. 73. £ 3 2 5§ - £ 8 -4 6§ + £ 1 0 2§ 74. 4c 3 5 -4 -1 2 6d + c -3 1 2 0 5 4d 75. c 2 1 5 9 8 2d - c 3 7 4 1d 76. c -3 2 4 8d c -1 2 0 5d 77. c -1 2 0 5d c -3 2 4 8d 78. £ 1 3 -6 2 0 5§ c 4 -1 8 2d 79. c 3 4 2 0 -1 6d £ -2 0 3 0 2 1§ 80. c 1 0 -2 1 4 -1 2 8d ≥ -1 2 0 1¥ 81. £ -2 0 3 5 1 -4 5 4 -1§ £ 1 -1 1 0 0 1 -1 0 -1§ 82. £ 0 7 10 1 -2 0 4 9 1§ c 3 2 1 -4 7 6d Find the inverse, if it exists, for each matrix. 83. c 2 5 1 3d 84. c -4 0 2 3d 85. £ 2 1 1 -1 0 -2 0 1 0§ 86. £ 2 -2 1 3 -3 4 5 -5 2§
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