Problem $8-8($Algo$)$

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, $87,552$; March, $69,120$; April, $100,000$; May, $40,000.$ Productivity is four units per worker hour, eight hours per day, $24$ days per month. Assume zero inventory on February $1.$ Costs are: hiring, $$52$ per new worker; layoff, $$72$ per worker laid off; inventory holding, $$12$ per unit$-$month; regular time labor, $$12$ per hour; overtime, $$18$ per hour; backorder, $$24$ per unit.

Develop a production plan and calculate the total cost of this plan. Note: Assume any layoffs occur at beginning of next month. Note: Leave the cells blank, whenever zero $(0)$ is required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.

$\backslash$table$[[,$February,March,April,May$],[$Forecast$,87,552,69,120,100,000,40,000],[$Beginning inventory,,,,$],[$Production required,,,,$],[$Production hours required,,,,$],[$Regular workforce,,,,$],[$Regular production,,,,$],[$Overtime hours,,,,$],[$Overtime production,,,,$],[$Total production,,,,$]]$