# Algebra Word Problem - Minimization of Cost

The area of a region was 125,000 square feet. A type of fencing costing \$20 per foot was used along the back and front, and a less expensive fence costing \$10 was used for the other sides. What were the dimensions of the region that minimized the cost of the fence?

I am not sure where to start with this question, my class has not done anything like this before.I started the equation with the function $$C=20(2x)+10(2y)$$ And then I used substitution to get $$C=40x+2500000/x$$ I am not sure how to solve this problem. I looked up an example problem similar; however, they used calculus to solve this and I am only in algebra. Does anyone know how to solve this without calculus?

• You probably noticed that dollar signs in a post do weird things. That is because it is used to initiate inline math mode for MathJax and $\LaTeX$. If you want a dollar sign to appear normally like \$, write it as \$ with the escape character \. – JMoravitz Mar 4 at 18:03
• Hint: use AM-GM. – Connor Harris Mar 4 at 18:04
• @ConnorHarris What's AM-GM? – Jake Miller Mar 4 at 18:20
• en.wikipedia.org/wiki/… – Connor Harris Mar 4 at 18:23
• Note that $Ax + \frac{B}{x} \geq 2 \sqrt{AB}$ with equality iff $Ax = \frac{B}{x}$. – Connor Harris Mar 4 at 18:28