4. (Chapter 3) Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements (in thousands of phones) as shown in the Table below, such as demand in Jan. is 1,000,000 units. Table: Monthly Demand for Cell Phones in Thousands Month January February March April May June July August September October November December Demand 1,000 1,100 1,000 1,200 1,500 1,600 1,600 900 1,100 800 1,400 1,700 Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 20 days a month, eight hours each day. One person can assemble a phone every 10 minutes. Workers are paid 20 euros per hour and a 50 percent premium for overtime. The plant currently employs 1,250 workers. Component costs for each cell phone total 20 euros. Given the rapid decline in component and finished-product prices, carrying inventory from one month to the next incurs a cost of 3 euros per phone per month. Skycell currently has a no-layoff policy in place. Overtime is limited to a maximum of 20 hours per month per employee. Assume that Skycell has a starting inventory of 50,000 units and wants to end the year with the same level of inventory. Assuming no backlogs, no subcontracting, and no new hires. a. Please construct an aggregate planning model. (Constructing an aggregate planning model means defining the decision variables and writing out the objective function and the constraints for the AP optimization problem.) Hint: You might want to use SOME of the following decision/planning variables for this problem: Ht = # of workers hired in month t (t = 1,..,12) Lt = # of workers laid-off in month t (t = 1,..,12) Wt = # of workers employed in month t (t = 1,..,12) Ot= # of hours of overtime in month t (t = 1,..,12) It= # of units (000s) held in inventory at the end of month t (t = 1,..,12) Ct = # of units (000s) subcontracted in month t (t = 1,..,12) Pt= # of units (000s) produced in month t (t = 1,..,12) b. What is the optimum production schedule? What is the annual cost of this schedule?