Question

Case Study In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were inspired by their teachers to start composting to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house, children convinced the Residents welfare association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of ₹ 50 per square metre for space so that there is no misuse of the space and Resident welfare association takes it seriously. Association hired a labourer for digging out 250 m3 and he charged ₹ 400 X (depth)2. Association will like to have minimum cost.

Value of h (in m) for which `(dC)/(dh) = 0` is

Options

• 1.5

• 2

• 2.5

• 3

Answer 1

2.5

Explanation:

Since,

`C = 12500/h + 400h^2`

∴ `(dC)/(dh) = (-12500)/h^2 + 800h`

Put `(dC)/(dh) = 0`

∴ `(-12500)/h^2 + 800h = 0`

`\implies` 800h³ = 12500

`\implies h^3 = 125/8`

`\implies h = 5/2`

`\implies` h = 2.5 m