Question 1086801
An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides.
let s = the side of the square base
let h = the height of the box
 The volume of a box is to be 18 cubic feet.
s * s * h = 18
s^2 * h = 18
s^2 = {{{18/h}}}
s = {{{sqrt(18/h)}}}
 The cost of material for the bottom is P10.00 per square foot and the cost of the material for the sides is P7.00 per square foot
Surface area:
S.A. = s^2 + 4(s*h)
Cost = 10s^2 + 7(4s*h)
C = 10s^2 + 28s*h
determine a model for the cost of the box as a function of its height h. 
Replace s with {{{sqrt(18/h)}}}
C(h) = 10{{{sqrt(18/h))^2}}} + 28*{{{sqrt(18/h)}}}*h
C(h) = 10({{{18/h}}}) + 28*{{{sqrt(18/h)}}}*h
simplify, extract the square root of 9
C(h) = 10({{{18/h}}}) + 28*{{{3sqrt(2/h)}}}*h
C(h) = {{{180/h}}} + {{{84sqrt(2/h)}}}*h
:
 what is the domain of the function, 
all positive values for h
:
:
Looks like this, y = Cost; x = height
{{{ graph( 300, 200, -6, 20, -100, 450, (180/x) + (84sqrt(2/x)*x)) }}}
minimum cost when height = 2, the side of the square base = 3
That would be 10(3^2) + 7(4*2*3) = $258