ok so i have this problem and i think ive got it figured just need a little help

we have a box with a square base and a volume of 4000cm^3

the sides and top cost 4.5$/m^2

the cost of the bottom is 7$/m^2

I am supposed to see how much it wil cost for minimum cost to make the box so...

Let x represent the length and width (since square base) let "y" rep height

V= 4000

4000=x^2y

y=4000/x^2

Than use surface area formula (including cost function?)

SA= 7(x^2) + 4.50(x^2) + 4.50 (4xy)

=11.50x^2 +18x(4000/x^2) (subbed Y value in from volume equation)

=11.50x^2 + 72000/x

than take derivitive

23x -72000/x^2

set to zero

23x^3 = 72000

x=14.6286?...

one more problem i have in the end..now how do i solve the problem of the cm^2 and the M^2 should i just divide the 4000 by 10000( or 1000 im not sure?) immediately or how should i deal with that?