Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers (service providers) to forecast the monthly demand (in thousands of phones) as shown in Table 3 below (e.g., demand in Jan. is 1,000,000 units.)

Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 22 days a month, eight hours each day. One person can assemble a phone every 15 minutes. Workers are paid 15 euros per hour and a 40 percent premium for overtime. The plant currently employs 1,500 workers. Component costs for each cell phone total 40 euros. Given the rapid increase in component and finished-product prices, carrying inventory from one month to the next costs 3.5 euros per phone per month. Overtime is limited to a maximum of 12 hours per month per employee. Assume Skycell has a starting inventory of 150,000 units and wants to end the year with the same level of inventory. Assume no backlogs. Skycell can subcontract (at a cost of 85 euros per unit), hire new workers (at a cost of 5,000 euros per new hire) or layoff existing workers (at a cost of 8,000 euros per worker).

Please construct an aggregate planning model. (i.e., define the decision variables and formulate/write out the objective function and the constraints for the Aggregate Planning optimization problem.)

Table 3 - Monthly Demand for Cell Phones, in Thousands

Month	Demand
January	1,000
February	1,100
March	1,000
April	1,200
May	1,500
June	1,600
July	1,600
August	900
September	1,100
October	800
November	1,400
December	1,700