An open tank with a square base and vertical sides is to be constructed form a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of tank is half its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in the question

Explanation

To solve the problem of minimizing the cost of constructing an open tank with a square base, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = side length of the square base of the tank
- \( h \) = depth of the tank
- \( V \) = volume of water the tank must hold (constant)

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