A large Omaha feed mill, B. Swart Processing, prepares its 6-month aggregate plan by forecasting demand for 50-pound bags of cattle feed as follows: January, 1,000 bags; February, 1,200; March, 1,250; April, 1,450; May, 1,400; and June, 1,400. The feed mill plans to begin the new year with no inventory left over from the previous year and backorders are not permitted. It projects that capacity (during regular hours) for producing bags of feed will remain constant at 800 until the end of April, and then increase to 1,100 bags per month when a planned expansion is completed on May 1. Overtime capacity is set at 300 bags per month until the expansion, at which time it will increase to 400 bags per month. A friendly competitor in Sioux City, Iowa, is also available as a backup source to meet demand-but can provide only 500 bags total during the 6-month period. Develop a 6-month production plan for the feed mill using the transportation method.
Cost data are as follows:
Regular-time cost per bag (until April 30) ....... $12.00
Regular-time cost per bag (after May 1) ....... $11.00
Overtime cost per bag (during entire period) ...... $16.00
Cost of outside purchase per bag ............ $18.50
Carrying cost per bag per month ............. $ 1.00