# Thread: Total cost of box as a function of x?

1. ## [SOLVED] Total cost of box as a function of x?

Hi,

I just started taking a Pre-Calculus math course in College. I took this course years ago and since then have forgotten most of what I have learned. I have come across the following question which I am stuck on.

A box with a square base has a volume of 600 cubic cm. If the material for the 4 sides and the top costs 5 cents per square cm and the material for the reinforced base costs 10 cents per square cm, express the total cost C of material (in cents) as a function of x, where x is the length of a side of the square base. Write the function in simplified form.

I have gotten this far:

$\displaystyle 600 = w^2*h$
$\displaystyle h = 600/w^2$

Area = $\displaystyle 2w^2 + 4*w(600/w^2)$
Area = $\displaystyle 2w^2 + 2400/w$

The answer that is given to me is $\displaystyle C(x) = 15x^2 + 12000/x$

I can see that if I multiply the 2400 by 5 I will get the $\displaystyle 12000/x$ but I don't understand where the $\displaystyle 15x^2$ comes from.

2. ## Re: Total cost of box as a function of x?

You need to multiply the parts through by 5 or 10 depending on their worth.

$\displaystyle \displaystyle C(x) = 5\times \left( x^2+ \frac{2400}{x}\right)+10\times \left( x^2\right) = \dots$

3. ## Re: Total cost of box as a function of x?

since the cost of top and base are different so you have to multiply top area with 5 and base area with 10 as
$\displaystyle C(x)=10x^2+5x^2+5(\frac{2400}{x})$

4. ## Re: Total cost of box as a function of x?

Thank you very much guys! Now it is clear to me Most impressive how quickly that was answered!