1. ## 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

2. 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 $LW = 500$ .

3. 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

4. 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.

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