Scenario $8\mathrm{.}2$ Willow

A company faces the aggregate planning problem shown in the table below. Cost of regular production is $$8$ per unit, the cost of producing the same unit on overtime is $$15,$ the cost of subcontracting is $$12$ per unit, and the cost of carrying a unit in inventory from one month to the next is $$6.$

$$ January February March April May

Forecast $4008001200700300$

Beginning Inventory $100$

Regular Time $$

Overtime $$

Subcontracting $$

Ending Inventory $$

The labor contract at the plant prohibits both overtime and subcontracting output to exceed $400$ units in any five$-$month window. The plant capacity is $20$ units per day produced using two shifts and the plant runs seven days a week. By policy, management wants to avoid stockouts.

What is the optimal total cost of the aggregate plan developed to address Scenario $8\mathrm{.}2?$

Question $44$ options:

A$)$

$$26,600$

B$)$

$$27,200$

C$)$

$$20,960$

D$)$

$$31,400$