Question 4 (5 points): Problem: The planner for the company that makes garden tractors is about to prepare an aggregate production plan that will cover the next six month. She has collected the following information: \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline Month & 1 & 2 & 3 & 4 & 5 & 6 & Total \\ \hline Forecast demand & 1000 & 2000 & 3000 & 4500 & 5500 & 2000 & 18000 \\ \hline \multicolumn{8}{|c|}{ Permanent Workforce: 140} \\ \hline \multicolumn{8}{|c|}{ Production per month: 2800 units or 20 per worker } \\ \hline \multicolumn{8}{|c|}{ Initial inventory: 1000 units } \\ \hline \multicolumn{8}{|c|}{ Desired inventory at the end of sixth month: 1000 units } \\ \hline \multicolumn{8}{|l|}{ Costs } \\ \hline \multicolumn{8}{|l|}{ Labous: } \\ \hline \multicolumn{8}{|c|}{ Regular time permanent: $100 per tractor } \\ \hline Overtime & \multicolumn{3}{|c|}{=$150 per tractor } & & & & \\ \hline Temporary & \multicolumn{3}{|c|}{=$100 per tractor } & & & & \\ \hline Hire cost & \multicolumn{4}{|c|}{ - $500 per temporary worker or $25 per unit } & & & \\ \hline Inventory & \multicolumn{4}{|c|}{\begin{tabular}{l} =$10 per tractor per month (charged on average \\ inventory level) \end{tabular}} & & & \\ \hline Back Order & & ryc & month & & & & \\ \hline \end{tabular} The planner wants to evaluate a production plan that calls for level output/workforce (with current level of permanent workforce, 140), using inventory to absorb the uneven forecast demand but allowing some back order