$10.$ DAT, Inc., needs to develop an aggregate plan for its product line. Relevant data are

production time $1$ hour per unit beginning inventory $500$ units

average labor cost $$10\mathrm{.}00$ per hour safety stock $(1/2)$ month

workweek $5$ days each day shortage cost $$20\mathrm{.}00$ per unit per month

$8$ hours each day

days per month $20$ workdays per month $($assuming$)$ carrying cost $$5\mathrm{.}00$ per unit per month

The forecast for next year is

jan $2500$

feb $3000$

mar $4000$

apr $3500$

may $3500$

jun $3000$

jul $3000$

aug $4000$

sep $4000$

oct $4000$

nov $3000$

dec $3000$

Management prefers to keep a constant workforce and production level, absorbing variations in demand through inventory excesses and shortages. Demand not met is car ried 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 you might use to test for a better solution. Make any necessary assumptions. $($Answer in Appendix D$)$