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?