In: Statistics and Probability
Units are per bag |
Standard Leather (square feet) |
Premium Leather (square feet) |
Cutting and Sewing Labor hours |
Finishing Labor Hours |
Profit |
Standard |
7 |
1 |
3 |
1 |
25 |
Deluxe |
0 |
9 |
4 |
2 |
65 |
Total available |
210 |
180 |
120 |
40 |
a. If the profit for Standard bags increases by $5/bag, does the optimal solution change? |
Explain why or why not. |
b. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
c. If the profit for Deluxe bags decreases by $5/bag, does the optimal solution change? |
Explain why or why not. (Note: this change is made WITHOUT changing the profit for |
Standard bags.) |
d. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
e. If the profit for Standard bags increases by $5/bag and the profit for Deluxe bags |
decreases by $5/bag, does the optimal solution change? (Hint: Use the 100% Rule) |
f. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
Units are per bag |
Standard Leather (square feet) |
Premium Leather (square feet) |
Cutting and Sewing Labor hours |
Finishing Labor Hours |
Profit |
Standard |
7 |
1 |
3 |
1 |
25 |
Deluxe |
0 |
9 |
4 |
2 |
65 |
Total available |
210 |
180 |
120 |
40 |
a. If the profit for Standard bags increases by $5/bag, does the optimal solution change? |
Explain why or why not. |
b. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
c. If the profit for Deluxe bags decreases by $5/bag, does the optimal solution change? |
Explain why or why not. (Note: this change is made WITHOUT changing the profit for |
Standard bags.) |
d. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
e. If the profit for Standard bags increases by $5/bag and the profit for Deluxe bags |
decreases by $5/bag, does the optimal solution change? (Hint: Use the 100% Rule) |
f. If the optimal solution does NOT change, will the value of the objective function at |
the optimal solution change? If it does, calculate the new profit. If it does not, explain why not. |
variables x1 x2 Description of the Problem
coefficient 30 5 x1 No. of standard bags to be produced.
profit (Z) 1200 x2 No. of delux bags to be produced.
The objective is to maximize profit.
constraints Objective function
1 210 <= 210 Max Z= 25 * x1 + 65 * x2 As the per unit profit on standard and delux bags is 25 and 65 respectively.
2 75 <= 180
3 110 <= 120 The above objective function is to be maximized subject to the following constraints.
4 40 <= 40 7x1<=210 (availability of standard leather)
For the given problem the optimal profit of $1300 can be earned by the producer by manufacturing 20 deluxe bags only. x1+9x2<=180 (availability of premium leather)
3x1+4x2<=120 (availability of cutting and sewing labour hours)
x1+2x2<=40 (availability of finishing labour hours)
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 3/5/2019 1:00:13 PM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$2 coefficient x1 0 0 25 7.5 17.77777778
$C$2 coefficient x2 20 0 65 160 15
1 a) Since the allowbale increase in x1 is 7.5 as per the sensitivity report, the increase of $5 in the profit due to x1 will not change the optimal solution.
1 b) The value of the objective function does not change as the coefficient of x1 is 0 in the optimal solution.
1 c) Since the allowbale decrease in x2 is 715 as per the sensitivity report, the decrease of $5 in the profit due to x2 will not change the optimal solution.
1 d) The value of the objective function does change as the coefficient of x2 is now changed to 60 from 65. The new objective function value is $1200.
1 e) The optimal solution will change as both the coefficients of x1 and x2 have been changed simultaneously. The new profit of $1200 can be earned by producing 30 standard bags and 5 deluxe bags
1 f) The value of the optimal function changes and the new objective function value is $1200.