Arectangular field will be fenced on all four sides. fencing for the north and south sides costs $6 per foot and fencing for the other two sides costs $5 per foot. what is the maximum area that can be included for $6000

The maximum area that can be included for $6000 is

Step-by-step explanation:

We can use the fact that the area of a rectangular field is given by the formula

where

= length of the field

= the width of the field

From the information given the total cost of rectangular field is

From the area formula we can say and substitute into the total area cost as follows:

And we solve for A, which is the maximum area

The equation we obtain is a parabola, for this reason we need to find the W-coordinate of the vertex.

and since