# Optimization Problem

• June 4th 2010, 11:54 AM
sam314159265
Optimization Problem
Hi, I'm having problems with the following question. It's probably super easy... but I just keep getting the wrong answer.

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 500m^2.
a) If a brick wall costs \$1200/m while a glass wall costs \$600/m, what dimensions would minimize the cost of the showroom?

When I try to solve for one of the variables I get, 2400L+1800W=500 Is this the right way to start it?

Any help would be appreciated
• June 4th 2010, 12:20 PM
Jester
Quote:

Originally Posted by sam314159265
Hi, I'm having problems with the following question. It's probably super easy... but I just keep getting the wrong answer.

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 500m^2.
a) If a brick wall costs \$1200/m while a glass wall costs \$600/m, what dimensions would minimize the cost of the showroom?

When I try to solve for one of the variables I get, 2400L+1800W=500 Is this the right way to start it?

Any help would be appreciated

What you want is to minimize $S = 1200(2L+W) + 600W$ subject to $LW = 500$ .
• June 4th 2010, 01:07 PM
sam314159265
So should I set the equation equal to zero? I tried that and got W=-3L/4, but when I plug that into A=LW and take the derivative to solve for W, I got W=8/3.... I'm not entirely sure what I'm doing wrong
• June 4th 2010, 01:12 PM
Jester
Quote:

Originally Posted by sam314159265
So should I set the equation equal to zero? I tried that and got W=-3L/4, but when I plug that into A=LW and take the derivative to solve for W, I got W=8/3.... I'm not entirely sure what I'm doing wrong

Using $LW = 500$, eliminate either $L$ or $W$ in $S$. This then gives a function of one variable. Now use calculus.
• June 4th 2010, 01:30 PM
sam314159265
This is probably going to sound dumb, but what is "S"? Thanks for helping me btw