I'm having trouble with this word problem if anyone can help me in detail with finding the function that would be great.
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A rectangular box is to have a square base and a volume of 70 ft3. The material for the base costs 34¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 29¢/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.
If x is one side of the base then what is the area of the base? If h is the height then what is the area of the four sides? What is the volume in terms of x and h? What is the volume as a number? So what equation can you make for the volume? (Solve this for h in terms of x.) What expression is the cost of the base? What expression is the cost of the sides? What expression is the total cost? (Plug in for h from the volume equation.) What expression is the total cost in terms just of x?
If you get stuck, please write back with your answers to my questions. Thanks!