Develop an aggregate production plan using each of the following guidelines and compute the total cost for each plan. Which plan has the lowest total cost?

A$.$ Use regular production at $100\%$ capacity each month. Supplement using inventory $($unlimited$),$ overtime, and subcontracting as needed. No backlogs are allowed. Overtime and subcontract can be used to build inventory.

B$.$ Use regular production at $100\%$ capacity each month. Use a combination of backlogs, subcontracting, overtime, and inventory $($unlimited$)$ to handle variations in demand. If used, overtime must be the same amount $($level$)$ for each month. If used, subcontracting must be the same amount $($level$)$ for each month. Overtime and subcontracting do not have to be equal. Overtime and subcontracting can be used to build inventory. If used, the max amount of backlog for any one period is $9$ units; backlog does not have to be the same each period.