SOLUTION: A rectangular box is to have a square base and a volume of 60 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top c

Algebra ->  Rectangles -> SOLUTION: A rectangular box is to have a square base and a volume of 60 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top c      Log On


   

Question 708794: A rectangular box is to have a square base and a volume of 60 ft3. The material for the base costs 40¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 30¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
f(x)= ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
How high is it? h = height
x^2h=60
h=60%2Fx%5E2

AREA OF SIDES
4%28hx%29=4%2860%2Fx%5E2%29x=60%2Fx
AREA OF BOTTOM
x%5E2
AREA OF TOP
x%5E2

COST OF THE BOX = f(x)
Uses the given prices.
f%28x%29=40%2Ax%5E2%2B10%2A60%2Fx%2B30%2Ax%5E2
Simplification, highlight%28f%28x%29=40x%5E2%2B600%2Fx%2B30x%5E2%29