### Home > PC > Chapter 7 > Lesson 7.2.1 > Problem7-40

7-40.

Farmer John has $300$ feet of fencing to enclose two identical rectangular pens with a common wall between them. Find the dimensions of the pens so that their areas are as large as possible. (Remember: Draw a diagram, define variables, write equations, identify the variable and write the variable to maximize in terms of one of the others. Then find an approximate solution by graphing.)

1. Write one equation with the $300$ feet of fencing for all of the sides.
2. Write another equation to maximize area: $A = xy$
3. Solve for one of the variables in the first equation and substitute in the second equation.
4. Use your calculator to find the place where the volume is the highest.