Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, 10,800; winter, 7,500; spring, 6,500; summer, 12,800. Inventory at the beginning of fall is 540 units. At the beginning of fall, you have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring if overtime is necessary to prevent stock-outs at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $90 for each temp; layoff, $180 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; regular time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In winter and spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in summer.

\begin{tabular}{|l|r|r|r|r|} \hline & \multicolumn{1}{|c|}{ Fall } & \multicolumn{1}{|c|}{ Winter } & \multicolumn{1}{|c|}{ Spring } & \multicolumn{1}{c|}{ Summer } \\ \hline Forecast & 10,800 & 7,500 & 6,500 & 12,800 \\ \hline Beginning inventory & 540 & & 0 & \\ \hline Production required & 10,260 & & 6,500 & \\ \hline Production hours required & 20,520 & & 13,000 & \\ \hline Production hours available & & & & \\ \hline Overtime hours & 0 & & 0 & \\ \hline Temp workers & 0 & 0 & 0 & \\ \hline Temp worker hours available & 0 & 0 & & \\ \hline Total hours available & & & & \\ \hline Actual production & & & & \\ \hline Ending inventory & & 0 & \\ \hline Workers hired & 0 & 0 & 0 & \\ \hline Workers laid off & 0 & 0 & 0 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|} \hline & & & Winter & Spring & \multicolumn{2}{|c|}{ Summer } \\ \hline \multicolumn{7}{|l|}{ Regular time } \\ \hline Overtime & & 0 & & ( & & 0 \\ \hline Inventory & & 0 & & & & 700 \\ \hline Backorder & & & & ( & & 0 \\ \hline Hiring & & 0 & & ( & & \\ \hline Layoff & & 0 & & ( & & \\ \hline Total & $ & 0 & $ & $ & $ & 700 \\ \hline Annual cost & & & & & $ & 700 \\ \hline \end{tabular}