Chapter 5

[Page 783 ( continued )]

1.	x 1 = 3, x 2 = 0, Z = 15
3.	(a) max. Z = 50 x 1 + 40 x 2 ; s.t. 3 x 1 + 5 x 2 150, 10 x 1 + 4 x 2 200, x i 0 and integer; (b) x 1 = 10, x 2 = 24, Z = 1,460
5.	(a) max. Z = 50 x 1 + 10 x 2 ; s.t. x 1 + x 2 15, 4 x 1 + x 2 25, x i 0 and integer; (b) x 1 = 6, x 2 = 1, Z = 310
7.	(a) max. Z = 50 x 1 + 40 x 2 ; s.t. 2 x 1 + 5 x 2 35, 3 x 1 + 2 x 2 20, x i 0 and integer; (b) x 1 = 4, x 2 = 4, Z = 360
9.	x 1 = 1, x 2 = 0, x 3 = 1, Z = 1,800
11.	min. Z = 81 x 1 + 50 x 2 ; s.t. 76 x 1 + 53 x 2 600, x 1 + x 2 10, 1.3 x 1 + 4.1 x 2 24, x 1 , x 2 0 and integer; x 1 = 6, x 2 = 3, Z = 636
13.	(a) max. Z = 85,000 x 1 + 60,000 x 2 - 18,000 y 1 ; s.t. x 1 + x 2 10,10,000 x 1 + 7,000 x 2 72,000, x 1 - 10 y 1 0, x 1 and x 2 0 and integer, y 1 = 0 or 1; (b) x 1 = 0, x 2 = 10, Z = 600,000
15.	min. Z = x 1 + x 2 + x 3 + x 4 + x 5 + x 6 ; s.t. x 6 + x 1 90, x 1 + x 2 215, x 2 + x 3 250, x 3 + x 4 65, x 4 + x 5 300, x 5 + x 6 125, x i 0; x 1 = 90, x 2 = 250, x 4 = 175, x 5 = 125, Z = 640
17.	(a) min. Z = 25,000 x 1 + 7,000 x 2 + 9,000 x 3 ; s.t. 53,000 x 1 + 30,000 x 2 + 41,000 x 3 200,000, (32,000 x 1 + 20,000 x 2 + 18,000 x 3 ) /(21,000 x 1 + 10,000 x 2 + 23,000 x 3 ) 1.5, (34,000 x 1 + 12,000 x 2 + 24,000 x 3 )/(53,000 x 1 + 30,000 x 2 + 41,000 x 3 ) 0.60 x 1 0, x 2 0, x 3 0 and integer; x 1 = 4, Z = $99,999.99; (b) x 1 = 2.9275, x 2 = .9713, x 3 = .383, Z = $83,433.65
19.	max. Z = 25,000 x 1 + 18,000 x 2 + 31,000 x 3 ; s.t. x 1 + x 2 + x 3 = 100, 5,000 x 1 + 11,000 x 2 + 7,000 x 3 700,000, x 1 10, x 2 10, x 3 10, x 1 , x 2 , x 3 0 and integer; x 1 = 20, x 2 = 10, x 3 = 70, Z = 2,850,000
21.	max. Z = 12,100 x 1 + 8,700 x 2 + 10,500 x 3 ; s.t. 360 x 1 + 375 x 2 + 410 x 3 30,000, x 1 + x 2 + x 3 67, 14 x 1 + 10 x 2 + 18 x 3 2,200, x 1 / x 3 2, x 2 / x 1 1.5, x 1 0, x 2 0 and integer, x 3 0; x 1 = 22, x 2 = 33, x 3 = 11, Z = $668,800 [Page 784]
23.	(a) max. Z = 1,650 x 1 + 850 x 2 + 790 x 3 ; s.t. 6.3 x 1 + 3.9 x 2 + 3.1 x 3 125, 17 x 1 + 10 x 2 + 7 x 3 320, x i 0 and integer; (b) x 1 = 10, x 3 = 20, Z = 32,300; rounded-down solution: x 1 = 13, x 3 = 12, Z = 30,930
25.	max. Z = 575 x 1 + 120 x 2 + 65 x 3 ; s.t. 40 x 1 + 15 x 2 + 4 x 3 600, 30 x 1 + 18 x 2 + 5 x 3 480, 4 x 1 2 x 2 0, x 3 = 20 y 1 , x 1 , x 2 , x 3 0 and integer, y 1 = 0 or 1; x 1 = 3, x 2 = 16, x 3 = 20, y 1 = 1, Z = $4,945
27.	(b) x 1 C = 1, x 3 D = 1, x 4 B = 1, x 5 A = 1, Z = 83 parts
29.	min. Z = 120 x 1 + 75 x 2 + 4.5 x 3 ; s.t. 220 x 1 + 140 x 2 + 12 x 3 6,300, 8 x 1 + 8 x 2 + x 3 256, .4 x 1 + .9 x 2 + .16 x 3 15, x 1 , x 2 0 and integer, x 3 0; x 1 = 28, x 2 = 0, x 3 = 11.67, Z = $3,412.50
31.	x 13 = 1, x 22 = 1, x 32 = 1, x 43 = 1, x 53 = 1, x 61 = 1, Z = $125 million
33.	max. Z = 127 x 1 + 83 x 2 + 165 x 3 + 96 x 4 + 112 x 5 + 88 x 6 + 135 x 7 + 141 x 8 + 117 x 9 + 94 x 10 ; s.t. x 1 + x 3 1, x 1 + x 2 + x 4 1, x 4 + x 5 + x 6 1, x 6 + x 7 + x 8 1, x 6 + x 9 1, x 8 + x 10 1, x 9 + x 10 1, x i = 0 or 1; x 2 = 1, x 3 = 1, x 5 = 1, x 8 = 1, x 9 = 1, Z = 618,000
35.	A(1,2,3), B(1,2,3), C(4,5,6), D(5,6,7), E(4,5,6), F(1,2,3), G(5,6,7), H(4,5,6), Z = 100 hr.
37.	max. Z = .9(3600) x A1 + .5(7200) x A2 + .9(2400) x B1 + .7(3600) x B2 + .95(3000) x C1 + .4(6000) x C2 + .95(3300) x D1 + .6(5400) x D2 ; s.t. x A1 + x A2 = 1, x B1 + x B2 = 1, x C1 + x C2 = 1, x D1 + x D2 = 1, .9 x A1 + .5 x A2 + .9 x B1 + .7 x B2 + .95 x C1 + .4 x C2 + .95 x D1 + .6 x D2 3, x ij x A2 = 1, x B2 = 1, x C1 = 1, x D1 = 1, Z = $4,035 per month