We have discussed in class aggregate planning using the following data:

$c_H=$$$500,$ cost of hiring one worker

$c_F=$$$1000,$ cost of firing one worker

$c_{\text{I}}=$$$80,$ cost of holding one unit of inventory for one month

$k=0\mathrm{.}14653$ units, aggregate units produced by one worker in one day

Suppose the demand forecast and workdays for the $12$ months next year are shown in the table

below. At the beginning of January, there will be $600$ units in inventory and $200$ workers.

a$)$ Please find the minimum constant workforce aggregate plan and the total cost of the plan.

b$)$ Please find the minimum inventory cost aggregate plan and the total cost of the plan.

c$)$ Please find the aggregate plan that minimizes the total cost.