ANSWERS A-19 67. ( ) , 1 2 1 3 69. Answers will vary. SECTION 6.8, PAGE 373 1. Half-plane 3. Solid 5. Ordered 7. Feasible 9. Objective 11. a) No b) Yes c) Yes d) No 13. (0, 1) (21, 0) 4 2 2 4 24 22 24 y . x 1 1 x y 15. x y 2 2 4 22 24 y $ 2x 2 6 6 26 (0, 26) (3, 0) 22 24 17. 2 4 24 22 24 x y (0, 22) (3, 0) 2x 2 3y . 6 19. x y 2 4 (0, 22) 4 24 22 24 ( , 0) 8 3 y $ x 2 2 3 4 21. x y 2 22 2 4 22 3x 1 2y , 6 (2, 0) (0, 3) 23. x y 2 4 6 2 4 22 24 (0, 5) (2, 0) 5x 1 2y $ 10 22 24 25. 24 22 2 4 24 22 4 x y y $ 22x 1 1 (0, 1) (1, 21) 27. x y 2 2 4 22 x 1 y . 0 (2, 22) (22, 2) 22 24 29. x y 2 22 2 4 8 22 24 4 y . x 2 4 x 1 y , 5 (0, 5) (0, 24) (4, 0) (5, 0) 6 6 31. y 2 4 y # 2x 1 5 x 2 y , 3 22 x 4 22 (3, 0) (0, 23) (0, 5) (5, 0) (4, 1) b) x 50 100 150 200 Cost ($) (100, 109) 50 100 150 200 Number of Miles C C 5 0.85x 1 24 C 5 0.79x 1 30 c) 100 miles 51. a) = + C x 15 400 = R x 25 b) x 400 200 600 800 1000 1200 1400 Amount ($) (40, 1000) 10 20 30 40 50 Number of Backpacks R 5 25x Cost Revenue C R C 5 15x 1 400 c) 40 backpacks d) = − P x 10 400 e) Loss of $100 f) 140 backpacks 53. a) = + = C x R x 15 4050, 40 b) x R C Amount ($) (162, 6480) 50 100 150 200 Number of Earbuds 5000 4000 3000 2000 1000 6000 7000 8000 C 5 15x 1 4050 R 5 40x c) 162 units d) = − P x 25 4050 e) Loss of $175 f) 185 units 55. + = + = x y x y 5 2 215 4 3 200 $35 for adult, $20 for student 57. + = x y 15 + = x y 0.40 0.10 0.25(15) l 7.5 of 40%, l 7.5 of 10% 59. a) y x 249 0.15 , = + $1700 b) Harbor Sales 61. = + = + y x y x 2.65 468.75 3.10 412.50 a) 125 square feet b) Home Depot 63. 7 hours 65. a) One unique solution; the lines intersect at one and only one point. b) No solution; the lines do not intersect. c) Infinitely many solutions; the lines coincide. y x 300 0.12 , = +
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