A company faces the following demands during the next three weeks: week 1, 20 units; week 2, 10 units; week 3, 15 units. The unit production costs during each week are as follows: week 1, $13; week 2,...

A company faces the following demands during the next three weeks: week 1, 20 units; week 2, 10 units; week 3, 15 units. The unit production costs during each week are as follows: week 1, $13; week 2, $14; week 3, $15. A holding cost of $2 per unit is assessed against each week’s ending inventory. At the beginning of week 1, the company has 5 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 3 weeks.

b. Revise the model so that the demands are of the form D_t
+ k∆_t
, where Dt is the original demand in month t, k is a factor, and ∆t is an amount of change in month t demand. (The Greek symbol ∆ is typically used to indicate change.) Formulate 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 ∆_t
’s. For example, try this when ∆₁= 2, ∆₂
=5, and ∆₃
=3. Describe the behavior you observe in the table. Can you find any “reasonable” ∆_t
’s that induce positive production levels in week 3?