A large St. Louis feed mill, Robert Orwig 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