Question: Problem 3. Consider the following LP min 2x1 + x2 s.t. X1 + x2 3 X1, X220 1) What are the shadow prices of the

Problem 3. Consider the following LP min 2x1 + x2

Problem 3. Consider the following LP min 2x1 + x2 s.t. X1 + x2 3 X1, X220 1) What are the shadow prices of the two constraints? Use simplex method to answer this question, and steps are required. (20 points) (Hint:(0,2) is an extreme point. You can write its corresponding BFS and start the simplex method from this BFS) 2) If I change the coefficient of x2 in the objective function from 1 to 1+4, what is the range of A so that the optimal basis in the original LP can be kept in the new LP? Use simplex method to answer this question, and steps are required. (15 points) 3) If I change the right-hand side of the first constraint from 2 to 2+, what is the range of A so that the optimal basis in the original LP can be kept in the new LP? Use simplex method to answer this question, and steps are required. (15 points) 4) Use Excel to verify your conclusion. Include the sensitivity report (name the sheet as "Prob3_Sensitivity Report") in your Excel table. (10 points) (Hint: solve the problem in Excel using Excel solver and capture its related sensitivity analysis.)

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