Optimization Problem

Feb 2010
12
0
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
 
Last edited:

Jester

MHF Helper
Dec 2008
2,470
1,255
Conway AR
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 \(\displaystyle S = 1200(2L+W) + 600W\) subject to \(\displaystyle LW = 500\) .
 
Feb 2010
12
0
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
 

Jester

MHF Helper
Dec 2008
2,470
1,255
Conway AR
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 \(\displaystyle LW = 500\), eliminate either \(\displaystyle L\) or \(\displaystyle W\) in \(\displaystyle S\). This then gives a function of one variable. Now use calculus.
 
Feb 2010
12
0
This is probably going to sound dumb, but what is "S"? Thanks for helping me btw