A farming company owns two farms, which differ in the growing of crops and their yields. Each farm has $25$ hectares available for cropping, and to fill pre$-$existing contracts, a total of at least $11,000$ bushels of wheat and $7000$ bushels of corn must be grown.

The Warialda farm yields $400$ bushels of wheat per hectare at a net cost of $$100$ per hectare, and $600$ bushels of corn per hectare at a net cost of $$120$ per hectare. The Warialda farm, which is less productive but has lower haulage expenses, yields $300$ bushels of wheat per hectare at a net cost of $$90$ per hectare, and $500$ bushels of corn per hectare at a net cost of $$110$ per hectare.

$($a$)$ Write down the problem as a linear programming problem

$($b$)$ Use the simplex algorithm to find a feasible solution to the problem $($not necessarily optimal$).$ You may use a calculator or computer programming language to perform the row reduction at each step, but you must explain your working $($e$.$g$.$ your row reductions, which variables you bring in and out of the basis and why$).$