Task: Shown below is a sensitivity report produced by Excel Solver for an LP problem with 3 decision variables (x_1, x_2, x_3) and 5 constraints (cons1, cns2,cons3, cons4, cons5).
Adjustable Cells
Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease
|
$C$4
|
x 1
|
750
|
0
|
2.5
|
1E+30
|
0.7
|
|
$D$4
|
x 2
|
200
|
0
|
1.2
|
1.3
|
1E+30
|
|
$E$4
|
x 3
|
50
|
0
|
1.8
|
0.7
|
1E+30
|
|
Constraints
|
|
|
|
|
|
|
Cell Name
|
Final
Value
|
Shadow
Price
|
Constraint Allowable Allowable R.H. Side Increase Decrease
|
|
$G$7 cons1
|
750
|
0
|
600
|
150
|
1E+30
|
|
$G$8 cons2
|
200
|
-1.3
|
200
|
150
|
200
|
|
$G$9 cons3
|
50
|
-0.7
|
50
|
150
|
40
|
|
$G$10 cons4
|
50
|
0
|
10
|
40
|
1E+30
|
|
$G$11 cons5
|
1000
|
2.5
|
1000
|
1E+30
|
150
|
Answer the following questions:
Question 1: If we increase the coefficient of x_2 in the objective function to 2.45, what would be the resultant optimal value of x_2?
Question 2: If we increase the coefficient of x_2 in the objective function to 2.6, what would be the resultant optimal value of x_2?
Question 3: By how much can the coefficient of x_2 be decreased without changing its LP optimal value?
Question 4: If the RHS constraint of cons3 is increased to 60, what would be the numerical change in the LP optimal value of the objective function?
Question 5: If the RHS constraint of cons4 is increased to 45, what would be the numerical change in the LP optimal value of the objective function?