ONLY SOLVE C

Exercise 10.7 (A dynamic single-item lot sizing problem) We consider the production of a single product over T periods. If we decide to produce at period t, a setup cost ct is incurred. For t 1, ...,T, let dt be the demand for this product in period t, and let Pt, ht be the unit production cost and unit storage cost (per period), respectively. (a) Formulate an integer programming problem in order to minimize the total cost of production, storage, and setup. (b) Suppose we allow demand to be lost in every period except for period T, at a cost of bt per unit of lost demand. Show how to modify the model to handle this option. (c) Suppose that production can occur in at most five periods, but no two such periods can be consecutive. Show how to modify the model to handle this option