Use the following information to develop aggregate plans.$$

Regular production cost $ $10$ per case

Regular production capacity $5,000$ cases

Overtime production cost $ $16$ per case

Subcontracting cost $ $20$ per case

Holding cost $ $1$ per case per month

Beginning inventory $0$

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$1.$Develop an aggregate plan using each of the following guidelines and compute the total cost for each plan. Note: Backlogs are not allowed.

a$.$Use level production. Supplement using overtime as needed.$($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

$$b$.$Use a combination of overtime $(500$ cases per period maximum$),$ inventory, and subcontracting $(500$ cases per period maximum$)$ to handle variations in demand.$($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

$$c$.$Use overtime up to $750$ cases per period and inventory to handle variations in demand.$($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$