it TWO FALL $2024$

$($i$)$

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 $100$ workers on January $31.$ You are given the following demand forecast: February, $83,328$; March, $67,200$; April, $100,080$; May, $40,080.$ Productivity is four units per worker hour, eight hours per day, $21$ days per month. Assume zero inventory on February $1.$ Costs are hiring, $$51$ per new worker; layoff, $$71$ per worker laid off; inventory holding, $$10$ per unit$-$month; straight$-$time labor, $$10$ per hour; overtime, $$15$ per hour; backorder, $$20$ per unit.

Develop a production plan and calculate the total cost of this plan. Note: Assume any layoffs occur at beginning of next month. $($Leave no cells blank $-$ be certain to enter $"$O$"$ wherever 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$,83,328,67,200,100,080,40,080],[$Beginning inventory,,,,$],[$Production required,,,,$],[$Production hours required,,,,$],[$Regular workforce,,,,$],[$Regular production,,,,$],[$Overtime hours,,,,$],[$Overtime production,,,,$],[$Total production,,,,$],[$Ending inventory,,,,$],[$Ending backorders,,,,$],[$Workers hired,,,,$],[$Workers laid off,,,,$]]$

$\backslash$table$[[$February$,$March,April,May,$],[$Straight time,,,,$],[$Overtime$,,,,],[$Inventory$,,,,],[$Backorder$,,,,],[$Hiring$,,,,],[$Layoff$,,,,],[$Total$,,,,],[$Total cost$,,,,]]$