Consider the following aggregate planning problem for one quarter.

Regular Time

Overtime

Subcontracting

Production$$ capacity$/$month

$1,000$

$200$

$150$

Production$$ cost$/$unit

$$$$5$

$$$$7$

$$$$8$

Assume that there is no initial inventory and a forecasted demand of$1,250$ units in each of the $3$ months. Carrying cost is$$ $$1$ per unit per month. Solve this aggregate planning problem for Production Manager Victor Shi using the transportation method.

Part $2$

Using the transportation method and assuming that backorders are not$$ permitted, the optimal total costequals$$$

$$

enter your response here $($enter your response as a whole$$ number$).$