A large Saskatchewan feed mill, B$.$ Swart Processing, prepares its six$-$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 $800$ 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 the expansion, at which time it will increase to $400$ bags per month. A friendly competitor in Alberta is also available as a backup source to meet demand $-$ but can provide only $500$ bags total during the six$-$month period.

Develop a six$-$month production plan for the feed mill using the transportation method.

Cost data are as follows:

$\backslash$table$[[$Regular$-$time cost per bag $($until April $30),$$$12\mathrm{.}00$