A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 440 feet of fencing to fence off the other three sides. What dimensions should the lot have if the enclosed area is to be a maximum?

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.

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