A$2.$ Plan production for the next year. The demand forecast is: apritg, $20000$ ; summor, $10,000$; fall, $15,000$; winter, $18,000.$ At the beginning of spring you heve $70$ worlors and $1,000$ units in inventory: The union contract specifies that you may lay of worbers only atace a your, at the beginning of summer. Also, you may hire new workers only at the end of summer to begis regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the start of fall shoukd result in planned prodoction levels for mumber and fall that equal the demand forecasts be summet and fall, respectively. If demend emonds supply, use overtime in spring only, which menns that backonders eon:$3$f oscur in winter. You are given quarter; backorder ecest, $$8$ per unit; straight$-$time labor, $$10$ per hour; avetime, $$15$ per hourProductivity is $0\mathrm{.}5$ unit per worker hour, eight hoes pes deg, $50$ days per quarter. Find the total cost.