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 determining the dimensions of an open tank with a square base that minimizes the cost of material while holding a fixed volume of water, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( x \) = width of the square base of the tank
- \( y \) = height (depth) of the tank
- \( V \) = volume of the tank (constant)

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