Problem $19-8($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, $80,640$; March, $69,120$; April, $100,240$; May, $40,240.$

Productivity is four units per worker hour, eight hours per day, $24$ days per month. Assume zero inventory on February $1.$ Costs are:

hiring, $$46$ per new worker; layoff, $$66$ per worker laid off; inventory holding, $$12$ per unit$-$month; straight$-$time labor, $$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 no cells blank $-$ be certain to enter $"0"$ wherever required. Negative values should be indicated by a minus sign.

Round your answers to the nearest whole number.