Replace the March demand forecast $510$ by C$.$

During a $46-$day period when there were $120$ workers, the firm produced $1,700,000$ cookies. Assume that there are $100$ workers employed, and C cookies in inventory at the beginning of month $1($January$).$ Further assume that the inventory carrying cost cI $=$ $$0\mathrm{.}10/$cookie$/$month$,$ employee hiring cost cH $=$ $$100/$work$,$ and cost of firing one worker cF $=$ $$200/$worker$.$ It is required that the inventory level at the end of month $12($December$)$ is $2$C$.$

$(2)$ Zero inventory plan $($chase strategy$)$: Find the optimal zero$-$inventory plan to meet all monthly demands, assuming that back order is not allowed. Compute the total cost of hiring and firing. In this case, inventory carrying cost should be zero $($except for the ending inventory$).$The Mr$.$ Meadows Cookie Company can obtain accurate forecasts for $12$ months based

on firm orders. These forecasts and the number of workdays per month are as follows: