Chapter 5.3, Problem 61E

In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.

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 mix $A$ costs $\text{\$}30$ per cubic yard and mix $B$ costs $\text{\$}35$ per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimal cost? What is this cost?