949 9.6 Systems of Inequalities and Linear Programming 73. 0 x y 4 2 –4 –4 4 74. 0 x y 2 1 –4 –1 75. Concept Check Write a system of inequalities for which the graph is the region in the first quadrant inside and including the circle with radius 2 centered at the origin, and above (not including) the line that passes through the points 10, -12 and 12, 22. 76. Cost of Vitamins The figure shows the region of feasible solutions for the vitamin problem of Example 5 and the straight-line graph of all combinations of capsules and chewable tablets for which the cost is $0.40. (a) The cost function is 10x + 20y. Give the linear equation (in slope-intercept form) of the line of constant cost c. (b) As c increases, does the line of constant cost move up or down? (c) By inspection, find the vertex of the region of feasible solutions that gives the optimal value. The graphs show regions of feasible solutions. Find the maximum and minimum values of each objective function. See Examples 4 and 5. 77. objective function = 3x + 5y x (5, 10) (2, 7) (6, 3) (1, 1) y 78. objective function = 6x + y x (6, 8) (1, 5) (9, 1) (1, 2) y Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. See Examples 4 and 5. 79. objective function = 3x + 5y 80. objective function = 5x + 5y 81. objective function = 10y 82. objective function = 3x - y Write a system of inequalities for each problem, and then graph the region of feasible solutions of the system. See Examples 4 and 5. 83. Vitamin Requirements Jane must supplement her daily diet with at least 6000 USP units of vitamin A, at least 195 mg of vitamin C, and at least 600 USP units of vitamin D. She finds that Mason’s Pharmacy carries Brand X and Brand Y vitamins. Each Brand X pill contains 3000 USP units of A, 45 mg of C, and 75 USP units of D, while each Brand Y pill contains 1000 USP units of A, 50 mg of C, and 200 USP units of D. x y A B C D 0 y = – x + 2 1 2 Region of feasible solutions x (7, 9) (1, 10) (7, 6) (1, 0) y
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