Problem 4 (modeling) A company must meet (on time) the following demands: . quarter 1: 30 units quarter 2: 20 units quarter 3: 40 units . Each quarter, up to 27 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. Excess production can be used in the following quarter, in which case a cost of $15 per unit is assessed against the quarter's ending inventory. a) Formulate an LP that can be used to minimize the total cost of meeting the next three quarters' demands. Assume that 20 usable units are available at the beginning of quarter 1. Clearly identify the meaning of variables in the LP model. b) Suppose now that of all units produced, 10% are defective and cannot be used to meet demand. After the quarter's demand is satisfied, 5% of any remaining units are distributed as a bonus to the employees. Any remaining units are stored as inventory at cost of $15 per unit and are available for the next quarter. Formulate an LP that can be used to minimize the total cost of meeting the next three quarters' demands. Assume that 20 usable units are available at the beginning of quarter 1. Clearly identify the meaning of the variables in the LP model