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, 1000 bags; February 1200; March 1250; April 1450; May 1400; and June 1400.
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 units until the end of April, and then increase to 1100 bags per month when a planned expansion is completed on May 1.
Overtime capacity is set at 300 bags per month until 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 only provide 500 bags total during the 6 months. 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