You are given the following demand forecast: February, $80,256$; March, $70,400$; April, $100,360$; May, $40,360.$ Productivity is four units per worker hour, eight hours per day, $22$ days per month. Assume zero inventory on February $1.$ Costs are: hiring, $$45$ per new worker; layoff, $$65$ per worker laid off; inventory holding, $$10$ per unit$-$month; regular time labor, $$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.

Note: Leave the cells blank, whenever zero $(0)$ is required. Negative values should be indicated by a minus sign. Round your