Miamitown Mulch is a small landscaping company whose primary retail sales are in three types of mulch. They sell Black Hardwood, Red Cedar, and Pine Bark mulch, typically in bulk to landscaping contractors. April, May and June are their three biggest sales months of the year, and they need to plan for the correct amount of mulch to have on hand each month. The supplier they get their mulch from requires firm contracts by March 1^st, and Miamitown needs to know how much to order for the coming months. Their estimates of demand, in tons, are as follows:

Black Red Pine

Month Hardwood Cedar Bark

April 400 300 250

May 700 400 300

June 375 325 175

The supplier can sell Miamitown up to 500 tons of Black Hardwood each month at $20 per ton. They can provide an additional 300 tons each month at $26 per ton. The supplier will provide as much as 350 tons of Red Cedar each month for $15 per ton, and as much as 150 more tons each month at $18 per ton. There is much greater availability of Pine Bark Mulch, so the supplier can provide Miamitown with up to 1000 tons per month, at a cost of $10 per ton.

Miamitown can hold a limited amount of inventory of mulch from one month to the next. The total amount that can be held, for all three types of mulch combined, cannot exceed 400 tons. They estimate that it will cost them 3% of the base price for each mulch, per ton, to hold mulch from one month to the next.

Formulate a linear program that will help Miamitown to schedule delivery of mulch necessary to meet anticipated demand, at the minimum cost possible.