Question

A rectangular box with a square base and an open top and a volume of 1ft^3 is to be made. Suppose the material used to build the sides cost $4 per ft^2 and the material used to build the bottom costs $1 per ft^2. Determine the dimensions (i.e. the side-length of the base and the height) of the box that will minimize the cost to build the box.

Note: if we let x denote the side-length of the base and let h denote the height, then the volume of the box is x^2h, which is required to be 1 (ft^3)

Answer 1

In this question first we find the cost function and then find its derivative and equate it to zero to find the dimension that will minimize the cost of the rectangular box. Hope you understand the solution.

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