Question

Asked Nov 7, 2019

A worker is to construct an open rectangular box with a square base and a volume of 48 ft^{3}. If material for the bottom costs $6/ft^{2 }and material for the sides costs $74/ft^{2 }what dimensions will result in the least expensive box? What is the minimum cost?

Let x be the length of one side of the base of the box. Express the total cost of the materials, C, in terms of x.

Step 1

Note: Please check the material cost for side. Because the dimension seems to be unrealistic since 74 is a large number.

Given that a worker is to construct an open rectangular box with a square base.

Step 2

To begin with,

Step 3

Since, the box is an open rectangle, the surface area of the...

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