1. Gang Aft Agley, a manufacturing company, faces the aggregate planning problem shown in the table below. Cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit, and the cost of carrying a unit in inventory from one month to the next is $2. The labor contract at the plant prohibits both overtime and subcontracting output to exceed 300 units in any five month window. The plant capacity is 600 units per month produced using two shifts, regardless of the number of days in a month. By policy, management wants to avoid stockouts. (a) Define and introduce decision variables. How many are they? (b) Define and introduce constraints. How many are they? (c) Define and introduce the objective function. (d) Which of these statements is evident without even developing an aggregate plan? i. Some overtime will be needed. ii. Ending inventory must be negative. iii. Overtime must exceed subcontracting. iv. Subcontracting must exceed regular time output. (e) Formulate and solve the problem using the Excel solver. Turn in your answers as well as the Excel file