Here's the problem I was asked: You are visiting your parents on a farm. They have asked you to design a small rectangular-shaped vegetable garden along an existing wall in their backyard. They wish to surround it with a small fence to protect their plants from animals. You have 15 yard of fencing to enclose the garden. The fencing is sold in .6 yard panels. In order to grow as many vegetables as possible, your task is to design a fence to enclose the maximum possible area. Partial panels of fencing may not be used.

Question

Here's the problem I was asked:  You are visiting your parents on a farm.  They have asked you to design a small rectangular-shaped vegetable garden along an existing wall in their backyard.  They wish to surround it with a small fence to protect their plants from animals.  You have 15 yard of fencing to enclose the garden.  The fencing is sold in .6 yard panels.  In order to grow as many vegetables as possible, your task is to design a fence to enclose the maximum possible area.  Partial panels of fencing may not be used.  
How many panels of fencing should you use along the width of the garden? and How many panels would you use along the length of the garden?

I am also to have an equation showing the maximum and minimum.

drwls · Answer

If each panel is 0.6 yards wide and you have fencing with 15 yards of width, you have 15/0.6 or 25 panels. 25 is an odd number; you need an even number of panels for a rectangle since you can't cut them. That means you use 24 panels and thrown one away. The best option would be 6 panels to a side, which would mean a square with side width 6x0.6 = 3.6 yards. The total area woould be 3.6^2 = 12.96 square yards. If you go with 7 x 5 panels, that would be 4.2 x 3.0 yards or 12.60 sq yd, which is not as good.

You did not need to use algebra to do this problem.

Seriously Worried · Answer

drwls, I don't think you really grasped the concept of answering this question.