A rectangular box is to have a square base and a volume of 70 ft3. The material for the base costs 4

A rectangular box is to have a square base and a volume of 70 ft3. The material for the base costs 4

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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 45¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 28¢/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.
601avery
24 January 2013
Let the side of the base be x. So the area of the base is x^2. The height of the box must therefore be 70/x^2. So now you have the dimensions of the box (albeit in terms of functions of x.) With the dimensions you can work out the area of base, sides and top, and therefore the cost of each of these components.
ianmoth
24 January 2013
Then differentiate the function and you can calulate x when dy/dx=0.
Priyanthi D.
27 January 2013
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