Problem $8-9($Algo$)$

Plan production for the next year. The demand forecast is: spring, $20,500$; summer, $9,800$; fall, $15,400$; winter, $17,600.$ At the beginning of spring, you have $64$ workers and $980$ units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means that backorders could occur in winter. You are given these costs: hiring, $$70$ per new worker; layoff, $$140$ per worker laid off; holding, $$19$ per unit$-$quarter; backorder cost, $$10$ per unit; regular time labor, $$12$ per hour; overtime, $$18$ per hour. Productivity is $0\mathrm{.}5$ unit per worker hour, eight hours per day, $50$ days per quarter.

Find the total cost of this plan. Note: Hiring expense occurs at beginning of fall.

Note: Leave the cells blank, whenever zero $(0)$ is required.

$\backslash$table$[[,$Spring,Summer,Fall,Winter$],[$Forecast$,20,500,9,800,15,400,17,600],[$Beginning inventory$],[$Production required$],[$Production hours required$],[$Regular workforce$],[$Regular production$],[$Overtime hours$],[$Overtime production,,,,$]]$