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, $1,100$ bags; February, $1,300$; March, $1,350$; April, $1,450$; May, $1,600$; and June, $1,600.$

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 $1,200$ bags per month when a planned expansion is completed on May $1.$ Overtime capacity is set at $400$ bags per month until the expansion, at which time it will increase to $500$ bags per month.

A friendly competitor in Sioux City, lowa, is also available as a backup source to meet demand $$ but can provide only $400$ 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:

Developing a $6-$month production plan for the feed mill using the transportation method, the total cost is $\backslash (\backslash$$ $\backslash )($enter your response as a whole number$).$