Answer question 2-C, 2-D, 2-E, 2-F 1 Microsoft Excel 16.0 Sensitivity Report 2 W
ID: 348823 • Letter: A
Question
Answer question 2-C, 2-D, 2-E, 2-F
1 Microsoft Excel 16.0 Sensitivity Report 2 Worksheet: [EXAM 1 excel.xlsx]Cool Dorm 3 Report Created: 10/25/2016 10:03:30 AM 4 Engine: Standard LP/Quadratic 6 Objective Cell (Max) 8 SE$9 Unit Profits Total Profit 10 Decision Variable Cells 2-c. Is the optimal solution degenerate? Explain why or why not 2-d. Is the optimal solution unique? Explain why or why not 2-e. How will raising the production of stands to its Cell Name Final Value 250 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease allowable increase affect the objection function total? 12 Cell 13 $B$8 Number to Make Stand 14 $CS8 Number to Make Cubes 15 16 Constraints 17 18 Name 1E+30 0.00 5.00 5.00 0.00 20 50 1E+30 10.0000002 2-f. Will the current solution remain optimal if finishing used is increased by 5 percent? Fina Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease Analyze and Explain Cell Name 9SDS12 Mold ProcessingUsed 20.00 0 20 SD$13 Finishing Used 21 SD$14 Stands Demand Used 20.00 0.00 40.00 6.25 5.00 0.00 36 1E+30 40 10 1E+30 16 40 32Explanation / Answer
2-c
None of the constraints have the allowable increase or allowable decrease equal to zero. Therefore, the solution is not degenerate.
2-d
One of the reduced cost is zero. Therefore, alternate optimal solutions exist.
2-e
No change in objective function will be observed as the shadow price (of the third constraint) is zero if the RHS is increased. But if the production quantity is changed from what it is at optimality, the profit will reduce because the optimal solution gives the maximum objective function (profit).
2-f
'Finishing used' cannot be changed in this way because the RHS is 40 which is already consumed. How will we increase the 'used' more than the RHS limit?
If the question is talking about the increase of RHS itself, then it can be answered. The allowable increase is 32. Here, the proposed increase is 5% i.e. 40 x 5% = 2 only. So, the objective will increase by 2 x 6.25 (shadow price) = 12.5. Since the coefficients of the objective function are constant, the optimal solution must change to incorporate this increase of 12.5