Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, $11,000$; winter, $8,000$ ; spring, $6,000$ ; summer, $13,000.$ Inventory at the beginning of fall is $500$ units.

At the beginning of fall you currently have $30$ workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated

with the union an option to use the regular workforce on overtime during winter or spring if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during

the fall. Relevant costs are hiring, $$100$ for each temp; layoff $$200$ for each worker laid off; inventory holding, $$5$ per unit$-$quarter; backorder, $$10$ per unit; straight time, $$5$ per hour; overtime, $$8$ per

hour. Assume that the productivity is $0\mathrm{.}5$ unit per worker hour, with eight hours per day and $60$ days per season.

a$.$ What is the total cost for this plan?

Relevant information includes:

Aggregate Production Planning Requirements