Chris Fisher, owner of an Ohio firm that manufactures display cabinets, develops an 8-month aggregate plan. Demand and capacity (in units) are forecast as follows:

The cost of producing each unit is $1,000 on regular time, $1,300 on overtime, and $1,800 on a subcontract. Inventory carrying cost is $200 per unit per month. There is no beginning or ending inventory is stock, and no backorders are permitted from period to period.
(a) Set up a production plan that minimizes cost by producing exactly regular time first, then overtime, and then subcontracting. This plan allows no backorders or inventory. What is this plan€™s cost?
(b) Through better planning, regular-time production can be set at exactly the same amount, 275 units, per month. Does this alter the solution?
(c) If overtime costs rise from $1,300 to $1,400, will your answer to part (a) change? What if overtime costs then fall to$1,200?

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Capacity Source (units) Jan. Feb. Mar. Apr. May June July Aug. Regular time 235 255 290 300 300 290 300 290 Overtime20 24 26 24 30 28 3030 Subcontract 12 16 15 17 17 19 19 20 Demand 255 294 321 301 330 320 345 340