Summary

The question asks for an optimal zero inventory plan $($chase strategy$)$ for a given table of monthly demands. It is stated that in $46$ workdays, $120$ workers are able to produce $1\mathrm{.}7$ million cookics. Using this information, $k$ is calculated, the amsount of cookics produced per day by a single worker. The initial amount of workers, w $0,$ inventory, in$,$ cost of inventory carrying. $Ci,$ cost of hiring, $Ch,$ and cost of firing. $Cf,$ are given as well as a requirement that inventory ar the end of month $12,$ i$12,$ be $514$

To solve this problem, the number of workers needed each month was computed using this formula: $w(j)D(j)+(kn(j)),$ where $w(j)$ is the number of workers, $D(j)$ is the demand, and $n$ is the number of workdays in a given month. This formula helps to decide the minimum mumber of workers needed each month to meet demands. The starting and ending inventories were factored in$.$ Invertory was calculated for each month using this formals:

$(0)=wnk+(j-1)-D(j),$ where $i(j)$ is inventory in a given month. The change in number of workers between months was calculated and added to the table based on whether workers were hired or fired. The values were added up and the cost of hiring and firiag were spplied to their respective sums to find the total cost of hiring and firing. The ending inventory was required to be $514,$ twice the amount of imitial inventory. This was assumod to mean greater than or equal to $514.$ Since this problem used the chase strategy, the cost of inventory carrying was applied to only the ending inventory. The tonal cost was equal to the sum of cost of hiring. firing, and inventory carrying.

Values given and computed:

$\backslash$table$[[$K$,307\mathrm{.}971],[$w$0,100],[$i$0,257],[Ci,0\mathrm{.}1],[Cb,100],[Cf,200]]$