Consider the following LP problem: Max 4X1-3X2+5X3 2Xi-3X3 S20 3X2+5X3 25 Using

Question

Consider the following LP problem: Max 4X1-3X2+5X3 2Xi-3X3 S20 3X2+5X3 25 Using the Excel Solver, one obtains the optimal objective value of 37 and the following Sensitivity Report Microsoft Excel 16.0 Sensitivity Report Report Created: 6/12/2017 4:27:59 PM Variable Cells Cell uS5 X1 SK$5 X2 L$5 X3 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 1.5 E+30 E+30 4 1E+30 8.8 -8.8 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease Cell SMS11 Constraint 3 Obj 5-0.6 5 205 10 3.5 13 20 1E 30 1. What is the optimal solutions for Xi Xa, and X? 2. Please answer following questions by circling Yes or No in the "Answer" column Question Answer 1. Will the optimal objective value still be 37 if the coefficient for X in the objective function increasesYesNo from 4 to 4.5? 2. Will the optimal solutions to Xi, X and Xa remain unchanged if the coefficient for X in the objectve YesNo function decreases from -3 to -5 3. Will the optimal solutions to Xi, X andX, remain unchanged if the coefficient for X, in the objective YesNo function increases from 5 to 9? Is constraint 1 binding under the optimal solution? 5. Is constraint 2 binding under the optimal solution? Yes No No raint 7. The shadow of constraint 3 will still be -0.6 if its RHS increases from 5 to 10?

Explanation / Answer

1. X1 = 8, X2 = 0, X3 = 1

2. 1. The answer is “No” as when x1 becomes 4.5 the objective function will become 4.5*8 + 5*1 = 41

2. The answer is “Yes” as X2 has an allowable increase of 8.8

3. The answer is “No” as x3 has an allowable increase of only 3.

4. The answer is “Yes” due to the fact that change in this constraint will change the optimal solution as well.

5. The answer is “No” due to the fact that change in this constraint will not change the optical solution.

6. The answer is “No” as the shadow price will remain 0.

7. The answer is “Yes” as the shadow price will not change and will remain -0.6

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