HW5_soln-1 - HW-5 Solution, IEOR162, Spring 09 SECTION 4.1...

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Unformatted text preview: HW-5 Solution, IEOR162, Spring 09 SECTION 4.1 1. max z = 3x1 + 2x2 s.t. 2x1 + x2 + s1 = 100 x1 + x2 + s2 = 80 x1 + s3 = 40 min z = 50x1 + 100x2 s.t. 7x1 + 2x2 - e1 = 28 2x1 + 12x2 - e2 = 243. min z = 3x1 + x2 s.t. x1 - e1 = 3 x1 + x2 + s2 = 4 2x1 - x2 = 3 2. 3. SECTION 4.4 1. From Figure 2 of Chapter 3 we see that the extreme points of the feasible region are Basic Feasible Solution H = (0, 0) s1 = 100, s2 = 80, s3 = 40 x1 = x2 = x3 = 0 E = (40, 0) x1 = 40, s1 = 20, s2 = 40 x2 = x3 = s3 = 0 F = (40, 20) x1 = 40, x2 = 20, s2 = 20 x3 = s1 = s3 = 0 G = (20, 60) x1 = 20, x2 = 60, s3 = 20 x3 = s1 = s2 = 0 D = (0, 80) s1 = 20, x2 = 80, s3 = 40 s2 = x1 = x3 = 0 2. From Figure 4 of Chapter 3 we see that the correspondence is as follows: Extreme Point E = (3.6, 1.4) B = (0, 14) C = (12, 0) Basic Feasible Solution x1 = 3.6, x2 = 1.4, e1 = e2 = 0 x2 = 14, e2 = 144, e1 = x1 = 0 x1 = 12, e1 = 56, x2 = e2 = 0 ...
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