An open top box with a square base of length x and height y

An open top box with a square base of length x and height y is to be constructed so that its volume is V = 3050 cm^3. If the cost of the material for the base of the box is dollar 0.39 per square centimeter and the cost of the sides is dollar 0.95 per square centimeter, express the cost C of the box in terms of the length of the base x.

Solution

V= 3050 cm^3

Volume of box = area of square *height = x^2*y

x^2 *y = 3050

So, y = 3050/x^2

Cost for base = x^2*0.39

Cost of sides = x*y*4*0.95 = 3.8xy

Cost of box = x^2 *0.39 + 3.8xy

sustitute y in terms of x:

Cost of box , in terms of x = 0.39x^2 +3.8x(3050)/x^2

C = 0.39x^2 + 11590/x^2