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HW_Solution_Chapter 04_EMSE102-202

# HW_Solution_Chapter 04_EMSE102-202 - 1 OR CHAPTER 4...

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1 OR CHAPTER 4 SOLUTIONS SECTION 4.1 1. max z = 3x 1 + 2x 2 s.t. 2x 1 + x 2 + s 1 = 100 x 1 + x 2 + s 2 = 80 x 1 + s 3 = 40 2. min z = 50x 1 + 100x 2 s.t. 7x 1 + 2x 2 - e 1 = 28 2x 1 + 12x 2 - e 2 = 243. 3. min z = 3x 1 + x 2 s.t. x 1 - e 1 = 3 x 1 + x 2 + s 2 = 4 2x 1 - x 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) s 1 = 100, s 2 = 80, s 3 = 40 x 1 = x 2 = x 3 = 0 E = (40, 0) x 1 = 40, s 1 = 20, s 2 = 40 x 2 = x 3 = s 3 = 0 F = (40, 20) x 1 = 40, x 2 = 20, s 2 = 20 x 3 = s 1 = s 3 = 0 G = (20, 60) x 1 = 20, x 2 = 60, s 3 = 20 x 3 = s 1 = s 2 = 0 D = (0, 80) s 1 = 20, x 2 = 80, s 3 = 40 s 2 = x 1 = x 3 = 0 2. From Figure 4 of Chapter 3 we see that the correspondence is as follows: Extreme Point Basic Feasible Solution E = (3.6, 1.4) x 1 = 3.6, x 2 = 1.4, e 1 = e 2 = 0 B = (0, 14) x 2 = 14, e 2 = 144, e 1 = x 1 = 0 C = (12, 0) x 1 = 12, e 1 = 56, x 2 = e 2 = 0 3. Basic Variables Basic Feasible Solution Corner Point x 1 , x 2 x 1 =150 x 2 =100 s 1 =s 2 =0 150, 100) x 1 , s 1 x 1 =200, s 1 =150, x 2 =s 2 =0 (200, 0) x 1 , s 2 x 1 =350, s 2 =-300, x 2 =s 1 =0 Infeasible x 2 , s 1 x 2 =400, s 1 =-450, x 1 =s 2 =0 Infeasible x 2 , s 2 x 2 =175, s 2 = 225, x 1 =s 1 =0 (0, 175) s 1 , s 2 s 1 =350, s 2 =400, x 1 =x 2 =0 (0, 0)

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2 SECTION 4.5 3. z x 1 x 2 x 3 s 1 s 2 s 3 RHS Ratio -------------------------------------------- 1 -2 1 -1 0 0 0 0 -------------------------------------------- 0 3 1 1 1 0 0 60 20 -------------------------------------------- 0 1 -1 2 0 1 0 10 10* Enter x 1 in row 2 -------------------------------------------- 0 1 1 -1 0 0 1 20 20 -------------------------------------------- -------------------------------------------- 1 0 -1 3 0 2 0 20 -------------------------------------------- 0 0 4 -5 1 -3 0 30 15/2 -------------------------------------------- 0 1 -1 2 0 1 0 10 None -------------------------------------------- 0 0 2 -3 0 -1 1 10 5* Enter x 2 in row 3 -------------------------------------------- z x 1 x 2 x 3 s 1 s 2 s 3 RHS Ratio -------------------------------------------- 1 0 0 3/2 0 3/2 1/2 25 -------------------------------------------- 0 0 0 1 1 -1 -2 10 -------------------------------------------- 0 1 0 1/2 0 1/2 1/2 15 -------------------------------------------- 0 0 1 -3/2 0 -1/2 1/2 5 -------------------------------------------- This is an optimal tableau with optimal solution z = 25, s 1 = 10, x 1 = 15, x 2 = 5, s 2 = s 3 = 0.
3 SECTION 4.6 2. z x 1 x 2 s 1 s 2 RHS ------------------------------- 1 1 1 0 0 0 ------------------------------- 0 1 -1 1 0 1 ------------------------------- 0 1 1 0 1 2 Enter x 2 in row 2 ------------------------------- ------------------------------- 1 0 0 0 -1 -2

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HW_Solution_Chapter 04_EMSE102-202 - 1 OR CHAPTER 4...

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