ANSWERS A-19 52. c) 4 8 12 16 4 8 12 16 x y (2, 5) (2, 2) (13, 5) (16, 2) 53. c) 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 18 x y 20 (20, 0) (4, 12) (0, 20) 54. c) x y 2 4 6 8 6 8 (8, 0) 2 (2, 3) 10 10 (0, 9) 55. + ≤ x y 1 2 200 ≤ y 1 2 150 ≥ x 0 ≥ y 0 x y (0, 0) (50, 300) (0, 300) (200, 0) 200 200 400 = + P x y 0.40 0.30 Maximum profit occurs at (50, 300). Thus, the manufacturer should make 50 lb of the all-beef hot dogs and 300 lb of the regular hot dogs for a profit of $110. 57. b) One example: + > x y 4 x y 1 + < SECTION 6.10, PAGE 399 41. (0, 3) (1, 2) 4 2 2 22 22 f(x) 52x 1 3 x y 4 42. (1, 3) (0, 1) 4 2 2 4 22 22 24 x y f(x) 5 2x 1 1 43. x y 22 2 24 22 24 2 4 (0, 2) (1, 21) f(x) 5 23x 1 2 44. 2 6 8 22 2 4 x y 22 24 (1, 7) (0, 5) f(x) 5 2x 1 5 4 45. 24 22 2 4 x 24 2 4 y f(x) 5 x 2 1 (2, 2) (0, 21) 2 22 3 46. 24 2 4 6 22 x 24 2 4 6 y (2, 2) (0, 3) 22 47. a) Upward b) = x 3 c) (3, 1) − 48. a) Upward b) = x 4 c) (4, 4) − 49. a) Downward b) x 6 = − c) ( 6, 169) − 50. a) Downward b) = x 6 c) (6, 53) 51. a) Downward b) = − x 5 4 c) ⎛ − ⎝⎜ ⎞ ⎠⎟ 5 4 , 33 8 52. a) Upward b) = x 11 8 c) 11 8 , 169 16 ⎛ − ⎝⎜ ⎞ ⎠⎟ 53. a) Upward b) = x 0 c) (0, 1) − d) (0, 1) − e) (1, 0), −( 1, 0) f) x y 1 2 23 24 2 3 4 f(x) 5 x2 2 1 (0, 21) 5 22 22 3 4 (21, 0) (1, 0) g) Domain: ;R range: ≥ − y 1
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