# Optimization Problem

#### 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

Last edited:

#### Jester

MHF Helper
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 $$\displaystyle LW = 500$$ .

#### 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

#### Jester

MHF Helper
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.

#### sam314159265

This is probably going to sound dumb, but what is "S"? Thanks for helping me btw