Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, $10,000$ ; winter, $8,000$ ; spring, $7,000$ ; summer, $12,000.$ Inventory at the beginning of fall is $500$ units: At the beginning of fall, you 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 backorders 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 worker productivity is $0\mathrm{.}5$ unit per worker hour, with eight hours per day and $60$ days per season.

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