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 x (in m) for minimum cost is

Options

• 5

• `10sqrt(5/3)`

• `5sqrt(5)`

• 10

Answer 1

10

Explanation:

For minimum cost, put `(dC)/(dh) = 0`, we get

h = 2.5 m

At `h = 2.5, (d^2C)/(dh^2) > 0`  ...(Hence, minimum)

Value of x at minimum cost

`x = sqrt(250/h)`

= `sqrt(250/2.5)`

= 10 m