# Optimization: optimization – #78

Question: A company must meet (on time) the following demands: quarter 1, 3000 units; quarter 2, 2000 units; quarter 3: 4000 units. Each quarter, up to 2700 units can be produced with regular-time labor, at a cost of $40 per unit. During each quarter, an unlimited number of units can be produced with overtime labor, at a cost of$60 per unit. Of all units produced, 20% are unsuitable and cannot be used to meet demand. Also, at the end of each quarter, 10% of all units on hand spoil and cannot be used to meet any future demands. After each quarter’s demand is satisfied and spoilage is accounted for, a cost of \$15 per unit is assessed against the quarter’s ending inventory. Determine how to minimize the total cost of meeting the next 3 quarters’ demands. Assume that 1000 usable units are available at the beginning of quarter 1.