Question

A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the surface area A of the box in terms of the width w of the base. If the material for the base and top costs 40 dollars/ft2 and that for the sides costs 50 dollars/ft2 express the total cost C as a function of the width.

Answer 1

Total cost F (w) = 160/w + 200* √(2w)

Explanation:

Volume in cubic feet

V (box) = x*y*w and square base means x=y so V= 2 = x^(2)*w

hence x^(2) = 2/w (1)

Area of base and top in square feet, and cost in $

Area(t+b) = 2*x*y = 2x^(2) C(1) = Cost of ( base + top) C(1) = 40*2x^(2)

C(1) =80*x^(2) and from eq. 1

C(1) = 80*2/w = 160/w

Area of sides = 4 * x* w = 4*√((2/w))*w

C(2) = Cost of sides. is: C(2)= 50*4*√((2/w))*w C(2) = 200* √2w

Total Cost = F(c) = 160/w +200*√2w