$4$

Problem $11-11($Static$)$

$20$ points

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.

$\backslash$table$[[$Period$,1,2,3,4,5,6,7,8,9,$Total$],[$Forecast$,190,230,260,280,210,170,160,260,180,1,940]]$

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.

Answer is complete but not entirely correct.

Total cost

$$13,815x$