Develop a production plan and calculate the annual cost for a

firm whose demand forecast is: fall, $10,900$; winter, $8,400$; spring,

$7,100$; summer, $12,900.$ Inventory at the beginning of fall is $545$

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

stock$-$outs at the end of those quarters. Overtime

is$$not$$available during the fall. Relevant costs

are hiring, $$80$ for each temp; layoff, $$160$ 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.$($Leave the cells blank, whenever zero $(0)$ is required.

Negative values should be indicated by a minus sign. Round up

"Number of temp workers, Workers hired and Workers laid off" to the

next whole number and all other answers to the nearest whole

number.$)$