Question 1078723
An open rectangular tank (with no top) is to have a square base and a volume of 100 cubic feet.
 The cost per square foot for the bottom is $16, and for the sides is $10.
 What are the dimensions of the cheapest tank?
:
Let x = the side of the square base
let h = the height of the tank
then
x^2 * h = 100 cu/ft
h = {{{100/x^2}}}
:
Surface area with no top
S.A. = x^2 + 4(h*x)
S.A. = x^2 + 4hx
Surface area cost
Total cost 
C = 16x^2 + 10(4hx)
C = 16x^2 + 40hx
replace h with {{{100/x^2}}}
C = 16x^2 + 40({{{100/x^2}}}*x
cancel x
C = 16x^2 + {{{4000/x}}}
Plot a graph of this equation, total cost is on the y axis
{{{ graph( 300, 200, -6, 20, -1000, 5000, 16x^2+(4000/x), 1200) }}}
You can see that minimum cost occurs when x = 5 ft 
Find the height
h = {{{100/5^2}}}
h = 4 ft is the height for minimum cost
Therefor the dimensions of the tank 5 by 5 by 4
Find the actual cost
C = 16(5^2) + 10*4(5*4)
C = 400 + 800
C = $1200, the green line on the graph