Chapter 5.2, Problem 47E

Plant food. A farmer can buy two types of plant food, mix $A$ and mix $B$. Each cubic yard of mix A contains $20$ pounds of phosphoric acid, $30$ pounds of nitrogen, and $5$ pounds of potash. Each cubic yard of mix $B$ contains $10$ pounds of phosphoric acid, $30$ pounds of nitrogen, and $10$ pounds of potash. The minimum monthly requirements are $460$ pounds of phosphoric acid, $960$ pounds of nitrogen, and $220$ pounds of potash. If $x$ is the number of cubic yards of mix $A$ used and $y$ is the number of cubic yards of mix $B$ used, write a system of linear inequalities that indicates appropriate restraints on $x$ and $y$. Find the set of feasible solutions graphically for the amounts of mix $A$ and mix $B$ that can be used.