1. Sensitivity analysis for RHS of constraint (and Shadow Price)

Consider the sensitivity analysis for a manufacturer of baseball gloves and catchers? mitts below.

1. Which of the constraints is(are) binding, and which not binding? How do you know this?
2. The units of constraints are hours. Suppose two workers in the cutting and sewing area call in sick for the week (assume a typical workweek for a person is 40 hours). ?Will the optimal solution change? Will the value of the objective function at the optimal solution change? Explain your reasoning.
3. Suppose that packaging and shipping is completed by two full-timers at 40 hours a week each, and one part-timer at 20 hours a week. It is the end of the school year, so you decide to hire the current part-timer as a full-timer for the summer (i.e., their hours are upped to 40 hours a week from the original 20). ?

Will your optimal solution change? ?Explain why or why not.

If your optimal solution does change, by how much will the profit change? ?(the objective function is to maximize profit.) Show your work to show how and why you got this.

4. Suppose that the finishers are composed of 6 full-time (40 hrs/week) workers and 3 part-time workers (20 hrs/week each). Again, since it is summer, you decide to hire the part-timers to be full-timers, so their hours are now 40 hrs/week.

What is the total increase in finishing time available in this case?

Will the optimal solution change? Explain why or why not.

If your optimal solution does change, by how much will the profit change? ?(the objective function is to maximize profit.) Show your work to show how and why you got this.

5. Suppose you have decided to hire all the part-timers as full-timers for the summer. Use the 100% rule to determine the change in profit, if possible If it is not possible to determine the change of profit at this point, explain how you came to that conclusion.

Constraints Cell Name $B$14 Amount produced Regular gloves 30314 Amount produced Catcher's mits Cell Name S8520 Cutting and Sewing Amount Used (LHS) $821 Finishing Amount Used (L-5) $B$22 Packaging and shipping Amount Used (LH6) Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 500 0 5 7 150 0 8 24000000007 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 725 900 1.00E+30 300 100 0 3 300 28 100 175 100 168.0000007 36 25