Applied Optimization Fence Question

Question

The owner of a lumber store wants to construct a fence to enclose a rectangular outdoor storage area adjacent to the store, using part of the side of the store (which is 210 feet long) for part of one of the sides.  There are 400 feet of fencing available to complete the job. Find the length of the sides parallel to the store and perpendicular that will maximize the total area of the outdoor enclosure.

Answer 1

It was given that the store side is 210 feet, and a rectangular enclosure will be built around that side of the store. The owner has 400 feet of fence.

 

Given that the enclosure will be a rectangle, the side opposite the store will be parallel to the store, and of the same length, namely 210 feet. So, 210 feet of fence will be used for that side of the rectangle.

 

There will be 400 - 210 feet, or 190 feet, left to construct the rest of the fence which will consist of two walls. The other two sides will be perpendicular to the store wall, and will therefore be equal in length.

 

When we divide the 190 feet by 2, we get 95 feet per wall.

 

So, there will be two walls of 95 feet, and one wall of 210 feet.