Answer
(a) see graph.
\begin{cases} x+y\leq500 \\ 90x+50y\leq40000\\30x+80y\leq30000\\x\geq0,y\geq0 \end{cases}
(b) Yes.
(c) NO.
Work Step by Step
(a) Assume the farmer plant $x$ acres of potatoes and $y$ acres of corn, we can set up the following inequalities:
\begin{cases} x+y\leq500 \\ 90x+50y\leq40000\\30x+80y\leq30000\\x\geq0,y\geq0 \end{cases}
We can graph the inequalities with the feasible region shown (solution).
(b) To check if the farmer can plant 300 acres of potatoes and 180 acres of corn, we locate the coordinate $(300,180)$ and see if the point fall in the solution region, and the answer is Yes.
(c) To check if the farmer can plant 150 acres of potatoes and 325 acres of corn, we locate the coordinate $(150,325)$ and see if the point fall in the solution region, it appears to fall on the purple boarder line. Plug the coordinates into the third equation above, we have $30\times150+80\times325=30500\gt30000$, so the answer is NO.
