$7.$ SummerFun, Inc., produces a variety of recreation and leisure products. The production manager has developed an aggregate forecast:

Month

Mar

Apr

May

Jun

Jul

Aug

Sep

Total

Forecast

$50$

$44$

$55$

$60$

$50$

$40$

$51$

$350$

Use the following information to develop aggregate plans.

Regular production cost $-$ $$80$ per unit

Overtime production cost $-$ $$120$ per unit

Regular capacity $-40$ units per month

Overtime capacity $-8$ units per month

Subcontracting cost $-$ $$140$ per unit

Subcontracting capacity $-12$ units per month

Holding cost $-$ $$10$ per unit per month

Back$-$order cost $-$ $$20$ per unit

Beginning inventory $-0$ units

Develop an aggregate 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. Supplement using inventory, overtime, and subcontracting as needed. No backlogs allowed.

b$.$ Use a level strategy. Use a combination of backlogs, subcontracting, and inventory to handle variations in demand.