Chapter 3

[Page 781 ( continued )] 5. 7. 9. 13. 15. 19. 27. 31. 37.

3.	Cells : B10:B12; Constraints: B10:B12 0, G6 F6, G7 F7; Profit: = B10 * C4+B11 * D4+B12 * E4; Target cell = B13.
(a and b) max. Z = 12 x 1 + 16 x 2 + 0 s 1 + 0 s 2 ; s.t. 3 x 1 + 2 x 2 + s 1 = 500, 4 x 1 + 5 x 2 + s 2 = 800, x i 0, s i
(a and b) c 1 , 12.8, 15 c 2 , 320 q 1 , 0 q 2 1,250; (c) $0, $3.20
(a) x 1 = 4, x 2 = 3, Z = 57, A: s 1 = 40, s 2 = 0, B: s 1 = 0, s 2 = 0, C: s 1 = 0, s 2 = 20; (b) x 1 = 2, x 2 = 4; (c) solution point same for profit = $15, new solution x 1 = 0, x 2 = 5, Z = 100 for profit = $20
11.	(a and b) max. Z = 2.25 x 1 + 3.10 x 2 + 0 s 1 + 0 s 2 + 0 s 3 ; s.t. 5.0 x 1 + 7.5 x 2 + s 1 = 6,500, 3.0 x 1 + 3.2 x 2 + s 2 = 3,000, x 2 + s 3 = 510, x i 0, s j
(a) Additional processing time, $0.75/hr.; (b) 0 c 1 2.906, 2.4 c 2 , 6,015 q 1 , 1,632 q 2 3,237, 0 q 3 692.308
(a) x 1 = 4, x 2 = 0, s 1 = 12, s 2 = 0, s 3 = 11, Z = 24,000; (b) x 1 = 1, x 2 = 3, Z = 28,500; (c) C still optimal
17.	(a and b) max. Z = 300 x 1 + 520 x 2 ; s.t. x 1 + x 2 = 410, 105 x 1 + 210 x 2 = 52,500, x 2 = 100, x i
(a) no, max. price = $80; (b) $2.095
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21.	(a) x 1 = 300, x 2 = 100, s 1 = 0 lb., s 2 = 15 lb., s 4 = 0.6 hr., Z = 230; (b) c 1 = $0.60, x 1 = 257, x 2 = 143, Z = 240; (c) x 1 = 300, x 2 = 125, Z = 242.50
23.	(a and b) min. Z = 50 x 1 + 70 x 2 ; s.t. 80 x 1 + 40 x 2 = 3,000, 80 x 1 = 1,000, 40 x 2 = 800, x i
25.	(a) personal interviews, $0.625/interview; (b) 25 c 2 , 1,800 q 1
(a) x 1 = 333.3, x 2 = 166.7, s 1 = 100 gal., s 2 = 133.3 gal., s 3 = 83.3 gal., s 4 = 100 gal., Z = 1,666; (b) any values of c
29.	max. Z = 1.20 x 1 + 1.30 x 2 ; s.t. x 1 + x 2 95,000, .18 x 1 + .30 x 2 20,000, x i
(a) 5%, $16,111.11; (b) x 1 = 0, x 2 = 66,666.7, Z = 86,666.67
33.	(a and b) min. Z = 400 x 1 + 180 x 2 + 90 x 3 s.t. x 1 200, x 2 300, x 3 100, 4 x 3 x 1 x 2 0, x 1 + x 2 + x 3 = 1,000, x i 0; (c) x 1 = 200, x 2 = 600, x 3 = 200, Z = 206,000
35.	max. Z = 0.50 x 1 + 0.75 x 2 ; s.t. 0.17 x 1 + 0.25 x 2 4,000, x 1 + x 2 18,000, x 1 8,000, x 2 8,000, x 1 , x 2 0; (b) max. Z = 0.50 x 1 + 0.75 x 2 ; 0.17 x 1 + 0.25 x 2 = 4,000, x 1 + x 2 = 18,000, x 1 = 8,000, x 2 = 8,000, x i 0.
x 1 = 8,000, x 2 = 10,000, Z = 11,500; (a) $375; increase, x 1 = 8,000, x 2 = 10,500, Z = $11,875; x 1 = 8,000, x 2 = 10,560, Z = $11,920
39.	(a) purchase land; (b) not purchase land
41.	(a) $0.78, 360 cartons; (b) $0; (c) x 1 = 108, x 2 = 54, x 3 = 162, Z = 249.48, no discount
43.	x 1 = 3, x 3 = 6, Z = 3,600; (a) more assembly hr.; (b) additional profit = $600; (c) no effect
45.	x 1 = 1,000, x 2 = 800, x 3 = 200, Z = 760; (a) increase by 100, $38 in additional profit; (b) x 1 = 1,000, x 2 = 1,000, Z = 770; (c) Z = 810; x 1 = 1,600, x 2 = 200, x 3 = 200
47.	x 1 = 20, x 2 = 33.33, x 3 = 26.67, Z = $703,333.4
49.	x 13 = 350, x 21 = 158.33, x 22 = 296.67, x 23 = 75, x 31 = 610, x 42 = 240, Z = $77,910
51.	max Z = 12 x 1 + 8 x 2 + 10 x 3 + 6 x 4 ; s.t. 2 x 1 + 9 x 2 + 1.3 x 3 + 2.5 x 4 74; 2 x 1 + .25 x 2 + x 3 + x 4 24; 2 x 1 + 5 x 3 + 2 x 4 36; 45 x 1 + 35 x 2 + 50 x 3 + 16 x 4 480, x i 0.