Plan production for a four$-$month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of $5,000$ hours of overtime labor per month in April and May $($zero overtime in February and March$).$ If demand exceeds supply, then backorders occur. There are $90$ workers on January $31.$ You are given the following demand forecast: February, $84,800$; March, $72,000$; April, $100,120$; May, $40,120.$ Productivity is five units per worker hour, eight hours per day, $20$ days per month. Assume zero inventory on February $1.$ Costs are hiring, $$51$ per new worker; layoff, $$71$ per worker laid off; inventory holding, $$11$ per unit$-$month; straight$-$time labor, $$12$ per hour; overtime, $$18$ per hour; backorder, $$22$ per unit.$\backslash$table$[[,$February,March,April,May$],[$Forecast$,84,800,72,000,100,120,40,120],[$Beginning inventory,$0,0,0,],[$Production required,$84,800,72,000,100,120,],[$Production hours required,$21,200,,,],[$Regular workforce,$133,,,],[$Regular production,$84,800,72,000,72,000,72,000],[$Overtime hours,$0,0,,0],[$Overtime production,$0,0,,0],[$Total production,$84,800,72,000,,72,000],[$Ending inventory,$0,0,,0],[$Ending backorders,$0,0,0,0],[$Workers hired,$0,0,0,0],[$Workers laid off,$0,0,0,0]]$