Cost of Material

[jaredld]

A rectangular box with volume 320 cubic feet is built with a square base and top. The cost is 1.50ft squared for the bottom, 2.50 feet squared for the sides, and 1 dollar a foot for the top. Let x= the length of the base, in feet. The sides of the top are x and the sides of the bottom are x.

So what I have so far is that by virtue of lwh= volume of a rectangle, the heighth of the rectangle is (8)(5^(1/2))/(x).

The problem wants you to
a.) Express the cost of the box as a function of x.
b.) Find the domain of the funtion.
c.) Graph the funtion.
d.) What dimensions minimize the cost of the box?

Any help would be greatly appreciated.

 

[Gene]

Well, you are starting with the proper box formula but I don't understand your height equation.
V = lwh = x^2h = 320 so
h = 320/x^2
That gives a cost formula =
1.50*x^2 for the bottom +
4*2.50*x*h for the 4 sides +
1.00*x^2 for the top
Using the h from above the cost in terms of x is
C = 1.5*x^2+4*2.5*x*(320/x^2)+x^2 =
2.5x^2+3200/x

 

[jaredld]

Thanks a lot. Sheesh that was pretty simple, but I couldn't see it. Actually the equation you got for the side was the same as mine, but I decided to square root the whole thing. Anyway, thankyou very much for your time.