Thread: 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.

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 $\displaystyle x$ feet, and the other side length be $\displaystyle y$ feet.

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

Area is $\displaystyle 3000$ sq ft, so:

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

Cost (which is to be minimised):

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

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

CB