A small company manufacturers bicycles in two different sized. David, the company's owner-manager, has just received the following forecasts for demands for the next six months.

a. Under what circumstances is it appropriate to develop just one aggregate production plan rather than two (one for each size bike)?
b. Suppose the forecasted demands for the two sizes of bikes are summed to obtain one aggregate forecast for each month. Currently David employs 27 full-time, highly skilled employees, each of whom can produce 50 bikes per month. Because skilled labour is in short supply in the area, David would like to keep his 27 workers permanently. There is no inventory' of finished bikes on hand at present, but David would like to have 300 on hand at the end of April. A maximum of 200 bikes can be produced during overtime each month. Determine the minimum cost aggregate plan and compute the total cost of your plan using these costs:

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16-inch Nov Dec. Jan Feb. Mar Apr. 20-inch 500 units 500 300 500 400 600 1,000 units 900 600 700 1,100 1,100 Regular Overtime $50 per unit $75 per unit Inventory Backorder $2.00 per unit per month $10.00 per unit per month