A flour mill buys its wheat from two different farms, then processes the wheat into flour. Wheat from Farm X costs the mill $8 per bushel, and wheat from Farm Y costs the mill $12 per bushel.

The selling price (in dollars per bushel) for the mill's wheat can be modeled by $\displaystyle {p}{\left({x},{y}\right)}$ = $\displaystyle {1500}-{x}-{y}$ where $\displaystyle {x}$ is the demand for the flour milled from Farm X's wheat and $\displaystyle {y}$ is the demand for flour milled from Farm Y's wheat. Assume that $\displaystyle {x}$ and $\displaystyle {y}$ may be zero (so the mill only buys from one of the suppliers) and that the mill can by 1/2 of a bushel.

Then the maximum profit is attained when
$\displaystyle {x}$ = Preview Question 6 Part 1 of 3   bushels
$\displaystyle {y}$ = Preview Question 6 Part 2 of 3   bushels
The amount of the flour mill's maximum profit is $ Preview Question 6 Part 3 of 3   .