Question

A rectangular box is to have a square base and a volume of 70  ft

3 . The material for the base costs  38¢/ft2, the material for the sides costs 10¢/ft2 , and the material for the top costs  27¢/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 1

`x-length\ of\ one\ side\ of\ base\\y-high\ of\ box\\x^2-area\ of\ base\\x^2y-volume\\\\x^2y=70\\y=(70)/(x^2)\ \ \ \ \ \ \ \ and\ x\\eq0\\\\38x^2+4\cdot10xy+27x^2\\65x^2+40xy\ in\ cents\\\\0.65x^2+0.4xy\ in\ dollars`