Question

An open tank with a square base is to be made to hold 4000 litres of water. What are the dimensions to make the cost minimum?

Answer 1

Answer:

Dimension of Tank = 20 * 20 * 10

Step-by-step explanation:

Volume = 4000

Let say Base side = b

& height = h

Volume = lbh = b²h

=> h = 4000/b²

Surface Area to be minimum for minimum cost

Surface Area = S = b² + 4bh

S = b²  +  4b * 4000/b²

S =b² + 16000/b

dS/db = 2b  - 16000/b²

2b  - 16000/b² = 0

=> b = 8000/b²

=> b³ = 8000

=> b = 20

d²S/db² = 2 + 32000/b³  is + ve

=> b = 20 will give minimum surface area

h = 4000/(20)² = 10

Dimension of Tank =  20 * 20 * 10