Let x represent side opposite to highway and y represent other two opposite sides as shown in the diagram.
The perimeter of the parking lot will be sum of 3 sides that is .
We have been given that the plan is to use 440 feet of fencing to fence off the other three sides. This means that perimeter of 3 sides is 440.
We know that area of rectangle is length times width, so area of parking lot will be
Upon substituting value of x, we will get:
Now we will find the derivative of area function as:
Let us find critical point by equating derivative to 0.
Now we will substitute this value is equation to solve for x as:
Therefore, the dimensions of 220 feet by 110 feet will enclose the maximum area.
