29. A company faces the following demands during the next three weeks: week 1, 2000 units; week 2, 1000 units; week 3, 1500 units. The unit production costs during each week are as follows: week 1, $130; week 2, $140; week 3, $150. A holding cost of $20 per unit is assessed against each week’s ending inventory. At the beginning of week 1, the company has 500 units on hand. In reality, not all goods produced during a month can be used to meet the current month’s demand. To model this fact, assume that only half of the goods produced during a week can be used to meet the current week’s demands.

a. Determine how to minimize the cost of meeting the demand for the next three weeks.

b. Revise the model so that the demands are of the form Dt + kCt, where Dt is the original demand (from above) in month t, k is a given factor, and Ct is an amount of change in month t demand. Develop the model in such a way that you can use SolverTable to analyze changes in the amounts produced and the total cost when k varies from 0 to 10 in 1-unit increments, for any fixed values of the Cs. For example, try this when C1 + 200, C2 + 500, and C3 + 300. Describe the behavior you observe in the table. Can you find any reasonable C’s that induce positive production levels in week 3?