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.

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 $"0"$ wherever required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.$)$