SOLUTION: A rectangular box is to have a square base and a volume of 30 ft^3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft^2, and the material for the top

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangular box is to have a square base and a volume of 30 ft^3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft^2, and the material for the top      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 874103: A rectangular box is to have a square base and a volume of 30 ft^3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft^2, and the material for the top costs 32¢/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.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Volume is yx%5E2=30 equivalent to y=30%2Fx%5E2.
Cost of top:32%2Ax%5E2
Cost of bottom: 44%2Ax%5E2
Cost of all sides: 4%2A10%2Axy

Cost of box: 32x%5E2%2B44x%5E2%2B400xy.
Substitute for y.
32x%5E2%2B44x%5E2%2B400x%2830%2Fx%5E2%29
highlight%28Cost=76x%5E2%2B12000%2Fx%29 cents.