1) A football coch has fenced in a rectangle shaped field with width 100 feet. and length 180 feet though he has a little extra land to spare. A team is planning to play football at his field for fundraising and he needs to make his area equal to the size of a regulation football field and have it fenced in. His original field is already fenced in. ( a regulation football field is 120 yards by 53 1/3 yards).

Company A charges $10 per linear foot to install new fencing and $6 per linear foot to remove old fencing plus $500 to repaint the football markings.

Company B charges $10 per linear foot to remove old fencing and $10 per linear foot to install new fencing. They will include the repaint of the football markings as a gift.

There are 3 parts to this problem.

1. Draw a diagram to show the renovation. (include a before and after view showing what is to be removed and what should be added, keep in mind that it may be cost effective to retain some of the old fencing.)

2. For each Company, show the total cost for this project.

3. If the coach has only $10,000 allotted for this project, which company should he select? Why?

First I drew a diagram with the original dimensions. Next, I divided 120 by 3 to get 40 feet and 53 1/2 by 3 to get 160/9 feet since 3 yards is 1 feet. I labeled the length and width of the new diagram with the new dimensions that I obtained after making the conversion. I made a particular observation that confuses me and that is the statement in the parenthesis indicating that, "it may be cost effective to retain some of the old fencing". Perhaps what's being implied is that it is only necessary to make a rectangle but the fencing that makes up the larger rectangle that houses the smaller rectangle can be retained. Is my conclusion correct? Provided that my assumption is valid then company B is more cost effective and the total cost should be

$578.80 correct? If my conclusion is false then where did my thinking go wrong?

A possible argument is that the area around the smaller rectangle would be impractical. Hence, why the area should be removed. But that would be absurd because the smaller area could just be removed later if it's no longer needed. Wouldn't it make more sense to remove the smaller area later as opposed to adding the larger area again?