To answer questions 1 to 4, turn to the worksheet labeled “Answer Report 1”. The “Final Value” column of the “Adjustable Cells” section informs you the optimal solution values. In other words, C&A should produce 400 units of BeltA and 300 units of BeltB. This is the answer to question 1.

The “Final Value” column of the “Target Cell” section of “Answer Report 1” informs you the optimal objective function value. In C&A’s case, the optimal profit is $25,000. This is the answer to question 2.

The “Status” column of the “Constraints” section of the “Answer Report 1” informs you which constraints are binding and not. In C&A’s case, there are two binding constraints which are the labor hours and BuckleA. There are two non-binding constraints which are BuckleB and leather. These are answers to questions 3 and 4 respectively.

The answers to questions 5 to 11 are found in the worksheet labeled “Sensitivity Report 1”. Question 5 asks about the new value for optimal profit if 1,100 hours of labor is available instead of 1000 hours. Check under the “Shadow Price” and “Allowable Increase” columns of the “Constraints” section of the sensitivity report. Notice that the shadow price and allowable increase for the labor constraint is $15 and 200 hours respectively. Since the increase in labor hours is 1100-1000 = 100 hours which is within the allowable increase limit of 200, the shadow price of $15 will hold. Thus, the increase in profit will be $15*100 = $1,500 bringing the new optimal profit to $25,000 + 1,500 = $26,500.

Question 6 asks about the new value for optimal profit if only 600 hours of labor is available instead of 1,000. In order to determine if the shadow price of $15 for labor is valid with a reduction of 1,000 – 600 = 400 hours, check under the “Allowable Decrease” column of the “Constraints” section for labor constraint. Since the allowable decrease is 600 hours, thus, a reduction of 400 hours is within the limit confirming that the shadow price is still $15. Thus, the reduction in profit will be $15*400 = 6,000 bringing the new optimal profit to $25,000 – 6,000 = $19,000.

Question 7 asks about the new optimal profit if only 200 units of BuckleB are available instead of 700. This implies a reduction of 700 – 200 = 500 units of BuckleB which exceeds the allowable decrease limit of 400 units. As a result, the new profit value cannot be determined since the shadow price of BuckleB is not known.

For question 8, an additional 100 units of BuckleA is within its allowable increase limit of 200. Thus, the shadow price of $25 will apply. The net increase in profit after subtracting a cost of $20 per BuckleA from its shadow price of $25 yields $5. Thus the increase in profit with an additional 100 units of BuckleA is $5 *100 = $500 bringing the new optimal value of profit from $25,000 to $25,000 + 500 = $25,500.

For question 9, the net increase in profit after subtracting a cost of $5 per BuckleA from its shadow price of $25 is $20. The allowable increase for BuckleA is 200. Thus, it is advised to bring in an additional 200 units of BuckleA because C&A’s profit will increase by $20*200 = $4,000.

Answers to questions 10 and 11 are found in the “Adjustable Cells” section of the sensitivity report as they are dealing with changes in the profit margin of the leather belts (or technically the coefficient of the decision variables in the objective function). For question 10, the new profit margin of BeltA is $10 impling a reduction of profit margin of $40 – 10 = $30. A $30 reduction in profit margin is beyond the allowable decrease of $25. Thus, the optimal production mix will change but its new value can only be determined by solving the problem again with the new profit margin figure.

For question 11, a $10 increase in profit margin for BeltB is within its allowable increase limit of $50. Thus, the optimal production mix of 400 units of BeltA and 300 units of BeltB will stay the same.