An Okra Farm Anticipates Highly Seasonal Demand for Their Product,tender

An okra farm anticipates highly seasonal demand for their product,tender pods of okra that can be made into the new drink sensation,the okra colada.Their estimate of the demand profile appears below.This forecast is based on the demand profile of last year's drink,the tuna colada.Once everyone in the test market had actually sampled the drink,demand fell to zero.
$$\begin{array} { | c | c | } \hline \text { Month } & \text { Demand Forecast } \\\hline \text { January } & 1,200 \\\hline \text { February } & 2,400 \\\hline \text { March } & 3,600 \\\hline \text { April } & 4,800 \\\hline \text { May } & 2,200 \\\hline \text { June } & 200 \\\hline\end{array}$$ The costs for the managerial levers appear in this table.
$\begin{array}{|l|c|}\hline \text { Item } & \text { Cost } \\\hline\text { Materials cost/unit } & \$ 10 \\\hline \text { Inventory holding cost/unit/month } & \$ 2 \\\hline \text { Marginal cost of stockout/unit/month } & \$ 5 \\\hline \text { Hiring and training cost/worker } & \$ 300 \\\hline \text { Layoff cost/worker } & \$ 500 \\\hline \text { Labor hours required/unit } & 4 \\\hline \text { Regular time cost/hour } & \$ 4 \\\hline \text { Over time cost/hour } & \$ 6 \\\hline \text { Beginning inventory equals } & 1000 \\\hline \text { Ending inventory greater than } & 500 \\\hline \text { Marginal subcontracting cost/unit } & \$ 30\\\hline\end{array}$ With a base price of $40 per bushel of okra and no promotion,what is the optimal sales and operations plan? Assume that the beginning workforce level is set at 80 workers.