A manufacturing firm would like to plan its production/inventory policy for the months of August, September, October and November. The product under consideration is seasonal, and its demand over the particular months is estimated to be 500, 600, 800 and 1200 units respectively. Presently, the monthly production capacity is 600 units with a unit cost of $25. Management has decided to install a new production system with monthly capacity of 1100 units with a unit cost of $30. However, the new system cannot be installed until the middle of November (hint: this timing restriction provides an important bounding criterion on the level of production activity for this month). Assume that the starting inventory is 250 units and that at most 400 units can be stored any given month. If the holding inventory cost per month per item is $3, find the production schedule that minimizes the total production and inventory cost using any LP software you choose. Assume that demand must be satisfied and that 100 units are required in inventory at the end of November. 1) Please formulate this problem.
2.) Solve with code