A company faces the following demands during the next four periods: 20, 10, 13 and 15 units. The unit production cost during each period is as follows: period 1: $10; period 2: 17; period 3: $15, period 4: $18. A holding cost at the rate of $2 per unit is assessed against each period’s ending inventory. At the beginning of period 1, the company has 3 units in the inventory. Because of the restriction of the warehouse, at the end of each period, there could be at most 5 units in inventory. a. Please have an LP model to minimize the total cost while meeting all demands on time.
b. Please solve the LP with Lindo, Excel or GUROBI.