For each problem, your responsibility is to formulate the decision environment as a mathematical model. You are not required to solve the problems! Simply write up the appropriate models. This, you should recall, will include complete descriptions of the decision variables, a statement of the objective function, and all relevant constraints. $($Note that constraints are not to contain $$IF$$ statements, OR statements, or multiplication or division of variables.$)$ Your models should be written in a form that I can interpret, not one that is meant for Excel.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 $400300250$

May $700400300$

June $375325175$

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.