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:

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

Regular$-$time cost per bag $($after May $1)$ $$11\mathrm{.}00$

Overtime cost per bag $($during entire period$)$ $$16\mathrm{.}00$

Cost of outside purchase per bag $,$$$18\mathrm{.}50$

Carrying cost per bag per month $$1\mathrm{.}00$

Please provide a solution for this :)