Hello, 2taall!

We use the same procedure of Minimization as for Maximization.

The tricky part (of course) is setting up the function to optimize.

I'll walk you thorough the set-up.

A rectangular box is to have a square base and a volume of 20 ft³.

The material for the base costs 30˘/ft², for the sides 10˘/ft², and the top 20˘/ft².

Determine the dimensions of the box that can be constructed at minimum cost. Code:

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x

The volume of the box is: . .**[1]**

The base has area ft². .Its cost is: . cents.

The top has area ft². .Its cost is: . cents.

The sides have area ft². .Their cost is: . cents.

Hence, the total cost is: . .**[2]**

Substitute [1] into [2]: .

Hence, we must minimize: .