[Page 781 ( continued )] 47. | 1. | x 1 = 4, x 2 = 0, Z = 40 | | 3. | (a) min. Z = .05 x 1 + .03 x 2 ; s.t. 8 x 1 + 6 x 2  48, x 1 + 2 x 2 12, x i 0; (b) x 1 = 0, x 2 = 8, Z = 0.24 | | 5. | (a) min. Z = 3 x 1 + 5 x 2 ; s.t. 10 x 1 + 2 x 2 20, 6 x 1 + 6 x 2 36, x 2 2, x i 0; (b) x 1 = 4, x 2 = 2, Z = 22 | | 7. | No labor, 4.8 lb. wood | | 9. | (a) max. Z = x 1 + 5 x 2 ; s.t. 5 x 1 + 5 x 2  25, 2 x 1 + 4 x 2 16, x 1 5, x 1 , x 2 0; (b) x 1 = 0, x 2 = 4, Z = 20 | | 11. | x 1 = 0, x 2 = 9, Z = 54 | | 13. | (a) max. Z = 300 x 1 + 400 x 2 ; s.t. 3 x 1 + 2 x 2 18, 2 x 1 + 4 x 2 20, x 2 4, x 1 , x 2 0; (b) x 1 = 4, x 2 = 3, Z = 2,400 | | 15. | (a) maximum demand is not achieved by one bracelet; (b) $600 | | 17. | x 1 = 15.8, x 2 = 20.5, Z = 1,610 | | 19. | A: s 1 = 4, s 2 = 1, s 3 = 0; B: s 1 = 0, s 2 = 5, s 3 = 0; C: s 1 = 0, s 2 = 6, s 3 = 1 | | 21. | A: s 1 = 0, s 2 = 0, s 3 = 8, s 4 = 0; B: s 1 = 0, s 2 = 3.2, s 3 = 0, s 4 = 4.8; C: s 1 = 26, s 2 = 24, s 3 = 0, s 4 = 10 | | 23. | changes the optimal solution | | 25. | x 1 = 28.125, x 2 = 0, Z = $1,671.95; no effect | | 27. | infeasible solution | | 29. | x 1 = 4, x 2 = 1, Z = 18 | | 31. | x 1 = 4.8, x 2 = 2.4, Z = 26.4 | | 33. | x 1 = 3.2, x 2 = 6, Z = 37.6 | | 35. | no additional profit | | 37. | (a) max. Z = 800 x 1 + 900 x 2 ; s.t. 2 x 1 + 4 x 2 30, 4 x 1 + 2 x 2 30, x 1 + x 2 9, x i 0; (b) x 1 = 5, x 2 = 5, Z = 8,500 | | 39. | x 1 = 5.3, x 2 = 4.7, Z = 806 | | 41. | (a) 12 hr.; (b) new solution: x 1 = 5.09, x 2 = 5.45, Z = 111.27 | | 43. | x 1 = 38.4, x 2 = 57.6, Z = 19.78; profit reduced | | 45. | (a) min. Z = .09 x 1 + .18 x 2 , s.t. .46 x 1 + .35 x 2 2,000, x 1 1,000, x 2 1,000, .91 x 1 .82 x 2 = 3,500, x 1 0, x 2 0; (b) 32 fewer defects | | x 1 = 160, x 2 = 106.67, Z = 568 | | 49. | x 1 = 25.71, x 2 = 14.29, Z = 14,571 | | 51. | (a) max. Z = .18 x 1 + .06 x 2 , s.t. x 1 + x 2 720,000, x 1 /( x 1 + x 2 ) .65, .22 x 1 + .05 x 2 100,000, x 1 , x 2 0 (b) x 1 = 376,470.59, x 2 = 343,526.41, Z = 88,376.47 | | 53. | one more hour for Sarah would reduce the regraded exams from 10 to 9.8; another hour for Brad has no effect | | 55. | only more Columbian would affect the solution; 1 lb of Columbian would increase sales to $463.20; increasing the brewing capacity has no effect; extra advertising increases sales | | 57. | infeasible |  |
