A nursery school wants to fence in a rectangular playground. one side of the playground is along a busy street, and needs taller fencing that costs $10 per foot. The fencing for the other three sides costs $7 per foot. If the school has a budget of $6000, what are the dimensions of the playground of largest area that they can build?

Could I just make one length x and the width y (or vice versa), solve for y, and use f(x) = x * y for the area, or would there be a problem since one side costs more than the others?

Question

A nursery school wants to fence in a rectangular playground. one side of the playground is along a busy street, and needs taller fencing that costs $10 per foot. The fencing for the other three sides costs $7 per foot. If the school has a budget of $6000, what are the dimensions of the playground of largest area that they can build?

Could I just make one length x and the width y (or vice versa), solve for y, and use f(x) = x * y for the area, or would there be a problem since one side costs more than the others?