Given the Projected Demands for the Next Six Months, Prepare $$\begin{array} { l l } \text { Month } & \text { Forecast } \\\hline 1 & 180 \\2 & 170 \\3 & 140 \\4 & 150 \\5 & 130 \\6 & 150\end{array}$$

Given the projected demands for the next six months, prepare an aggregate plan that uses inventory, regular time and overtime, and back orders. The plan must wind up with no units in ending inventory in period 6. Regular time capacity is 150 units per month. Overtime capacity is 20 units per month. Overtime cost is $30 per unit, back order cost is $20 per unit, inventory holding cost is $5 per unit, regular time cost is $20 per unit, and beginning inventory is zero. $$\begin{array} { l l } \text { Month } & \text { Forecast } \\\hline 1 & 180 \\2 & 170 \\3 & 140 \\4 & 150 \\5 & 130 \\6 & 150\end{array}$$