An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of the material will be least when depth of the tank is half of its width.

Explanation

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

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

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