DAT Inc., needs to develop an aggregate plan for its product line. Relevant data are Production time $=1h\frac{r}{?}$ unit; average labor cost $=$$$\frac{10}{h}r$; work week $=5$ days, $8h\frac{r}{?}$ day; days per month $=20$; beginning inventory $=500$ units; safety stock $=$ one$-$half month; shortage cost $=$ $$20/$unit$/$month; carrying cost$=$$$5/$unit$/$month$.$

The forecast for next year is

$\backslash$table$[[$Jan$,$Feb,March,April,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 carried 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 solution; just find a good solution and state the procedure you might use to test for a better solution. Make necessary assumptions.

$[10$ Marks$]$