Solution to Final Exam Fall 2008

Page 1 of 6

Department of Operations and Information Management

OPIM 621: Decision Models & Uncertainty

Fall 2008

Solution to Final Examination

1. Foresight Co. (15 points)

a. (2 points) Under the optimal plan, the total production cost in May is…

(x) $163,875

The total production cost in May is ($17.25)*(9,500) = $163,875.

b. (4 points) Foresight has discovered that its inventory costs will be higher in February. They will increase from $.65 to $.85. Which one of the following statements holds?

i)

The optimal production-inventory plan will…

(x) change.

Since the allowable increase for February inventory cost is $.15, a

$.20 increase is beyond the allowable range. Therefore, the solution will change (i.e., switch to a new optimal corner point of the feasible region.) ii)

The cost of the new optimal plan will…

(x) increase by less than $700.

If we stay with the original optimal production-inventory plan, the cost will increase by exactly $700 = ($.2)*(3,500). However, the new optimal plan must result in a cost increase below $700. (Otherwise, the plan would stay the same.)

c. (3 points) The optimal production-inventory plan would change, if the production capacity in

January decreased by…

(x) any amount.

January production capacity is a binding constraint. Hence, any change in production capacity, no matter how small, will cause the optimal solution values to change.

d. (3 points) Another producer has offered to sell Foresight 500 units which would be delivered for sale in June. The maximum total cost that Foresight should be willing to pay for the 500 units is at most…

(x) $8,975.

OPIM621 Decision Models & Uncertainty

Solution to Final Exam Fall 2008

Page 2 of 6

The shadow price for the June balance equation is $17.95.

The

allowable decrease is 1,500 units, so 500 is well within the range.

These 500 units would be worth ($17.95)*(500) = $8,975.

e.

(3 points) Suppose Foresight could increase the production capacity for the month of

February by exactly 9,000 units for a total fixed cost of $1,200. Should this be done?

(x) It can’t be determined from the sensitivity report.

The shadow price for February capacity is -$.15 and the allowable increase is 7,000. Hence, the benefit (i.e., cost reduction) from the first 7,000 units is ($0.15)*(7,000) = $1,050.

We know that beyond 7,000 units, the shadow price cannot be more negative than -$.15. Therefore, the benefit from the last 2,000 unit increase cannot be more than ($.15)*(2,000) = $300. However, if the constraint becomes non-binding with a shadow price of zero, the additional benefit will be zero.

In sum, the actual benefit is between $1,050 and $1,350. Thus, we need to rerun the LP to determine whether or not it should be done.

2. The C3 Company (16 points)

a) (5 points) Formulate a linear program to help C3 determine the optimal production schedule for the next three-year planning horizon. Use the