A-49 Answers to Selected Exercises 37. x y 0 x + y ≥ 0 2x – y ≥ 3 1 1 –3 39. x y 0 2x + y > 2 x – 3y < 6 6 –2 2 41. y x 3 5 0 3x + 5y ≤ 15 x2 + y2 < 9 43. x y 4x – 3y ≤ 12 y ≤ x2 3 –4 45. y x 2 –1 4 x + 2y ≤ 4 y ≥ x2 – 1 1 47. x y ≤ (x + 2)2 y ≥ –2x2 4 2 –2 y 0 49. x x + y ≤ 36 –4 ≤ x ≤ 4 6 12 36 y 0 51. The solution set is ∅. 53. x 3x – 2y ≥ 6 x + y ≤ –5 y ≤ 4 4 –3 –5 –5 2 0 y 55. x –2 < x < 2 y > 1 x – y > 0 –2 2 –2 2 1 y 0 57. x x ≤ 4 x ≥ 0 y ≥ 0 x + 2y ≥ 2 1 1 y 0 59. y x 6 –3 4 –2 2x + 3y ≤ 12 2x + 3y > –6 3x + y < 4 x ≥ 0, y ≥ 0 Solution set 61. x 1 –1 y y ≥ – 1 y > x3+ 1 63. x –2 1 4 y y ≤ ( ) x y ≥ 4 1 2 65. x y ≤ log x y ≥ zx – 2z 2 2 y 0 Solution set 67. 3x + 2y ≥ 6 −10 −10 10 10 69. x + y ≥ 2, x + y ≤ 6 −10 −10 10 10 71. x + 2y … 4 3x - 4y … 12 73. x2 + y2 … 16 y Ú 2 75. x 70 y 70 x2 + y2 … 4 y 73 2 x - 1 77. maximum of 65 at 15, 102; minimum of 8 at 11, 12 79. maximum of 66 at 17, 92; minimum of 3 at 11, 02 81. maximum of 100 at 11, 102; minimum of 0 at 11, 02 83. Let x = the number of Brand X pills and y = the number of Brand Y pills. Then 3000x + 1000y Ú 6000, 45x + 50y Ú 195, 75x + 200y Ú 600, x Ú 0, y Ú 0. x y 75x + 200y = 600 45x + 50y = 195 3000x + 1000y = 6000 8 2 1 6 3 0 85. 300 cartons of food and 400 cartons of clothes; 6200 people 87. 8 of cabinet A and 3 of cabinet B; 100 ft3 89. 3 3 4 servings of A and 1 7 8 servings of B; $1.69 9.7 Exercises 1. 2; 0 3. 6; -1; -1; 12 5. 3 * 6 7. 2 * 2; square 9. 3 * 4 11. 2 * 1; column 13. a = 0, b = 4, c = -3, d = 5 15. x = -4, y = 14, z = 3, w = -2 17. This cannot be true. 19. w = 5, x = 6, y = -2, z = 8 21. z = 18, r = 3, s = 3, p = 3, a = 3 4 23. Be sure that the two matrices have the same dimension. The sum will have this dimension as well. To find the elements of the sum, add the corresponding elements of the two matrices. 25. c -2 17 -5 4d 27. c -2 10 -7 -2 7 7d 29. The sum does not exist. 31. c -6 4 8 2d 33. £ 4 -5 4§ 35. The difference does not exist. 37. D -23 4 -1 -13 -225 -22T 39. c 5x + y 6x + 2y y x + 3yd 41. c -4 0 8 6d 43. c -9 6 3 0d 45. c 14 -12 2 6d 47. c -1 2 -3 -3d 49. yes; 2 * 5 51. no 53. yes; 3 * 2 55. c 13 25d 57. c -17 -1d 59. c 1722 3523 -422 2623 d
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