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# hw7 - 0 1 = X 3 0 3.75 0 0-4 0-1.75-0.25 1 5 = S 4...

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I.E.2001 OPERATIONS RESEARCH ( Homework Assignment 7: Due Thursday, Mar. 18, 2010 ) Question 1 . Consider the following linear program: Minimize Z = 50X 1 + 20X 2 + 30X 3 + 80X 4 st 1) 400X 1 + 200X 2 + 150X 3 + 500X 4 800 2) 3X 1 + 2X 2 6 3) 2X 1 + 2X 2 + 4X 3 + 4X 4 10 4) 2X 1 + 4X 2 + X 3 + 5X 4 8 X 1 , X 2 , X 3 , X 4 0. 1. Solve the problem using LINDO or the Solver add-in to MS-Excel . Then answer the following: a. What are the shadow prices corresponding to Constraints 1, 2 and 4? Clearly interpret these values. b. What happens to the value of the objective in each of the following three different cases (1) c 2 =18, (2) c 3 =50 (3) b 2 =4? c. By how much can b 3 change before the current basis is affected? How (if at all) is the objective affected? d. Give two interpretations of the reduced cost corresponding to the nonbasic variable X 4 . 2. The optimal tableau (with Z * =90) is shown below: Z X 1 X 2 X 3 X 4 S 1 S 2 S 3 S 4 RHS Basic 1 -27.5 0 0 -50 0 -2.5 -7.5 0 90 = Z 0 137.5 0 0 350 1 62.5 37.5 0 50 = S 1 0 1.5 1 0 0 0 -0.5 0 0 3 = X 2 0 -0.25 0 1 1 0 0.25 -0.25
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Unformatted text preview: 0 1 = X 3 0 3.75 0 0 -4 0 -1.75 -0.25 1 5 = S 4 Referring to the tableau, answer the following: a. What would happen to Z if S 2 is increased by 1 units? b. Suppose we were maximizing (as opposed to minimizing), so that the above tableau is suboptimal, and suppose X 1 is chosen to enter into the basis. Interpret the substitution rates of the basic variables with respect to X 1 . Based on your answer, which variable would leave the basis? Why? Without any pivoting, find the value of Z after the next iteration. Question 2. Answer Question 1 on page 254 (Review problems for Chapter 5) of the text (HAL Computers). Question 3. Answer Question 16 on page 261 (Review problems for Chapter 5) of the text (Cornco). Define variables for production, sales and inventory of each product in each period, and for the total raw material required - assume that the availability of the raw material is for the entire 3-month period....
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