Thinking Mathematically 141

Math Exercise:

A small farm has 70 acres of space to plant.  The farmer wants to grow green beans and corn.  It costs $60 per acre to grow the corn and $30 per acre to grow the green beans.  The farmer has $1800 to use for plating the vegetables.  It takes the farmer 3 days of plant each acre of corn and 4 days to plant each acre of green beans.  There are 120 days available to plant the vegetable.  When the farmer sells the vegetables, he can expect to make a profit of $180 per acre for the corn and $100 per acre for the green beans.  How many acres should the farmer allow for each vegetable in order to maximize profit?