Problem $11-11($Static$)$

A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast

of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively

high in periods $3$ and $4,$ and again in period $8,$ as can be seen from the following forecasts.

The department now has $20$ full$-$time employees, each of whom produces $10$ units of output per period at a cost of $$6$

per unit. Beginning inventory for period $1$ is zero. Inventory carrying cost is $$5$ per unit per period, and backlog cost is

$$10$ per unit per period.

The manager has decided to use part$-$time workers to assist during seasonal peaks. The cost per unit, including hiring

and training, is $$11.$ The output rate is $10$ units per worker per period for all workers. A maximum of $10$ part$-$time

workers can be used, and the same number of part$-$time workers must be used in all periods that have part$-$time

workers. The ending inventory in period $9$ should be $10$ units. The limit on backlogs is $20$ units per period. Try to make

up backlogs as soon as possible. Compute the total cost for this plan. Assume $20$ full$-$time workers and regular

monthly production $=$ regular capacity.