# Using the following information, develop an optimum (minimum total cost) six-month aggregate plan 4 Total 1500 + n Month Forecast (units) 400 300 100 150 250 300 + n Beginning inventory of the first month-n Costs Output Regular time cost- S120 per unit Overtime cost \$180 per unit Inventory holding cost \$50 per unit per month on average inventory Back order cost = \$200 per unit per month Average Inventory = (Beginning Inventory + Ending Inventory) / 2 Regular output 22 units per worker per month Overtime output maximum of 90 units per month for the entire company (all workers combined) Ending inventory for the sixth month 0 Strategy:Maintain workers and use ove ime Example: Sixth Month’s Forecasted Demand 300 + n = 300 45-345 units Total Forecasted Demand = 1500 + n = 1500 + 45 = 1545 units Beginning Inventory n- 45

Total cost calculation for this six-month aggregate plan:
If n=48
Total Cost calculation of the Plan Total
Month 1 2 3 4 5 6
Forecast 400 300 100 150 250 348 1,548
Beginning Inventory 48 0 0 88 158 128
Production Required (forecast -Inventory+ backorders of previous month) 352 342 132 62 92 220
Regular Production (10 workers *22 units) 220 220 220 220 220 220 1,320
Overtime Production (maximum 90 units/month) 90 90 0 0 0 0 180
Total Production (regular + Overtime) 310 310 220 220 220 220 1,500
Ending Inventory 0 0 88 158 128 0
Average Inventory (Beginning + Ending)/2 24 0 44 123 143 64
Ending Backorders 42 32 0 0 0 0
Cost:
Regular cost of production (\$120/unit) \$26,400 \$26,400 \$26,400 \$26,400 \$26,400 \$26,400 \$158,400
Overtime cost of production (\$180/unit) \$16,200 \$16,200 \$0 \$0 \$0 \$0 \$32,400
Inventory holding cost (\$50/unit per period) \$1,200 \$0 \$2,200 \$6,150 \$7,150 \$3,200 \$19,900
Backorder cost (\$200/ unit per period) \$8,400 \$6,400 \$0 \$0 \$0 \$0 \$14,800
Total Cost per Month \$52,200 \$49,000 \$28,600 \$32,550 \$33,550 \$29,600 \$225,500
A. Back log for the second month = 32
B. Ending inventory for third month = 88
C. Average inventory for fifth month =143
D. Total cost of the third month = \$28,600
E. Total inventory holding cost for this six-month aggregate plan = \$19,900
F. Total cost for this six-month aggregate plan = \$225,500

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