Problem $8-7($Algo$)$

Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, $10,300$; winter, $7,600$; spring, $6,600$;

summer, $12,300.$ Inventory at the beginning of fall is $515$ units. At the beginning of fall, you have $35$ 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 oftion to use the regular workforce on overtime during winter or spring if overtime is necessary to prevent stock$-$outs 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; regular 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. In each quarter, produce to the full output of

your regular workforce, even if that results in excess production. In winter and spring, use overtime only if needed to meet the

production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of

reducing the number of temp workers in summer.

Note: Leave the cells blank, whenever zero $(0)$ is required. Negative values should be indicated by a minus sign. Round up "Temp

workers", "Workers hired", and "Workers laid off" to the next whole number and all other answers to the nearest whole number.

Problem $8-7($Algo$)$

Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, $10,300$; winter, $7,600$; spring, $6,600$;

summer, $12,300.$ Inventory at the beginning of fall is $515$ units. At the beginning of fall, you have $35$ 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 stock$-$outs 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; regular 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. In each quarter, produce to the full output of

your regular workforce, even if that results in excess production. In winter and spring, use overtime only if needed to meet the

production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of

reducing the number of temp workers in summer.

Note: Leave the cells blank, whenever zero $(0)$ is required. Negative values should be indicated by a minus sign. Round up "Temp

workers", "Workers hired", and "Workers laid off" to the next whole number and all other answers to the nearest whole number.