# Math Help - Optimization Problem.

1. ## Optimization Problem.

Hey guys, I think I know the procedure, but something about my answer is wrong. Can someone post a solution for this?

A showroom for a car dealership is to be built in the shape of a rectangle with brick on the back and sides, and glass on the front. The floor of the showroom is to have an area of 500 meters squared. If a brick wall costs $1200/m while a glass wall costs$600/m, what dimensions would minimize the cost of the showroom?

2. ## Re: Optimization Problem.

A better idea is for you to show us your own solution and we'll check where your mistake is...

3. ## Re: Optimization Problem.

Let x be the length of the showroom and y the width. We know that the area xy=500m², so y=500/x.

3 walls will be built with brick and just 1 will be of glass, so:

C(x)=1200x+1200x+1200y+600y= 2400x+1800y= 2400x+1800(500/x)= 2400x+900000/x

Now just find the derivative of C(x) and solve C'(x)=0.

4. ## Re: Optimization Problem.

What you have done is correct. Why do you think it's wrong?