[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 | |