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$.$

$(1)$ use the Constant workforce plan $($level strategy$)$: Find the minimum constant workforce needed to meet all monthly demands $($i$.$e$,$ back order not allowed$).$ Computer the total cost including employee hiring or firing cost $($which occurs only at the beginning of month $1),$ and inventory carrying cost.