# Story Problem - Minimum Total Cost

• Nov 9th 2008, 08:36 PM
killasnake
Story Problem - Minimum Total Cost
Can someone help me set up this story problem, I am having trouble.

A Landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing$10 per foot along the fourth side. Find the minimum total cost to enclose this region.
• Nov 10th 2008, 12:27 AM
CaptainBlack
Quote:

Originally Posted by killasnake
Can someone help me set up this story problem, I am having trouble.

A Landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing$10 per foot along the fourth side. Find the minimum total cost to enclose this region.

Give names to the unknows in the problem. In this case let the length of the side to be fenced be $x$ feet, and the other side length be $y$ feet.

Now express the conditions in the problem in terms of thse unknowns:

Area is $3000$ sq ft, so:

$x \times y=3000 \ \ \ \ ...(1)$

Cost (which is to be minimised):

$c=10x + 25\times 2\times y +25x= 35x+50y\ \ \ \ ...(2)$

now use $(1)$ to eliminate one of the variables form $(2)$ leaving you with a function of one variable to be minimised.

CB