$$

$\backslash$table$[[$Production time,$1$ hour per unit,Beginning inventory,$500$ units$],[$Average labor cost,$$10$ per hour,Safety stock,One$-$half month$],[$Workweek$,5$ days, $8$ hours,Backorder cost,$$20$ per unit per$],[,$each day,,month$],[$Days per month,Assume $20$ workdays,Carrying cost,$$5$ per unit per$],[,$per month,,month$]]$

The forecast for next year is

$\backslash$table$[[$JAN$.,$Feb.,MAR.,APr.,MAY,June,JULY,AUg.,SEPt.,OCt.,Nov.,DeC.$],[2,500,3,000,4,000,3,500,3,500,3,000,3,000,4,000,4,000,4,000,3,000,3,000]]$

Management prefers to keep a constant workforce and production level, absorbing variations in demand through inventory excesses and shortages. Demand not met is carri over to the following month.

Develop an aggregate plan that will meet the demand and other conditions of the problem. Do not try to find the optimum; just find a good solution and state the procedure might use to test for a better solution. Make any necessary assumptions.