1. Gang Aft Agley a manufacturing company tries to do aggregate planning and got an estimation of its total cost for next year. The monthly demand data Di, where i= 1,2,3... and 12 I for the next year is given. The manufacturing company currently employs W6 workers. It takes a worker 5 hours to make a unit and workers are pad $15/hour. The company works 20 days a month , 8 hours a day. The material cost is 100$.unit. The marginal cost (excluding material cost) of subcontracting is $80/unit. The inventory at the beginning is I0 units.
   1. Assuming no new hires no layoffs , and no overtime by the policy. No stockout is allowed and the month ending inventory cannot exceed 25% of the demand in that month.

The decision variables are defined as follows:

Wt: workforce size for month t, 1=1, ...,12

pi: number of units produced in month t, t-1, ...12

It: inventory at end of the month t, H=1, ..,12

Ct: number of units subcontracted in month t, 1=1, ...12

1.a 1a. Formulate the total cost that the company is trying to minimize. Substitute data where applicable :

1.b. What are the constraints?

1.c Assuming the company aims for a chase strategy , the cost of hiring is CH and the cost of layoff is Ci per worker. What decision variables should be added?

1.d.What changes should be made in the formulation from part 1a and 1b (both objective function and constraints)