946 CHAPTER 9 Systems and Matrices Step 2 Figure 24 shows the region of feasible solutions formed by the inequalities 8x + 2y Ú 16, x + y Ú 5, 2x + 7y Ú 20, x Ú 0, and y Ú 0. Step 3 The vertices are 10, 82, 11, 42, 13, 22, and 110, 02. Steps 4 See the table. The minimum cost of $0.70 occurs at 13, 22. and 5 x y (0, 8) (1, 4) (3, 2) (10, 0) 0 8x + 2y ≥ 16 x + y ≥ 5 2x + 7y ≥ 20 x ≥ 0 y ≥ 0 Figure 24 Vertex Cost =10x +20y 10, 82 10102 + 20182 = 160 11, 42 10112 + 20142 = 90 13, 22 10132 + 20122 = 70 110, 02 101102 + 20102 = 100 Vertices are from Figure 24. 70 cents, or $0.70, is the minimum cost. Robin’s best choice is to take 3 capsules and 2 chewable tablets each day, for a minimum cost of $0.70 per day. She receives just the minimum amounts of vitamins B1 and C, and an excess of vitamin A. S Now Try Exercise 89. 9.6 Exercises CONCEPT PREVIEW Match each system of inequalities with the correct graph from choices A–D. 1. x Ú 5 y … -3 2. x … 5 y Ú -3 3. x 75 y 6 -3 4. x 65 y 7 -3 A. 0 –3 5 x y B. 0 –3 5 x y C. 0 –3 5 x y D. 0 –3 5 x y CONCEPT PREVIEW Fill in the blank(s) to correctly complete the sentence, or answer the question. 5. The test point 10, 02 ________________ satisfy the inequality -3x - 4y Ú 12. (does / does not) 6. Any point that lies on the graph of -3x - 4y = 12 ________________ lie on the graph of -3x - 4y 712. (does / does not) 7. What are the coordinates of the point of intersection of the boundary lines in the following system? x Ú 2 y … -5
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