Question

a wholesaler of pencils charges rs 24 per dozen on order of 50 dozensor less. for orders in excess of 50 dozens. the price is reduced by 20 paise per dozen in excess of 50 dozen find the size of the order that maximise his total revenue. ​

Answer 1

Given:

Price of pencils per dozen = 24

Price reduced for more than 50 dozens = 20p

To Find:

Size of the order maximizing his total revenue

Solution:

Let the number of dozens in an order = x

Thus,  

When x< 150, TR = 24x

When x> 50, price per dozen will be -

p = 24 - 0.20(x-50)  

= 34 - 0.20x

Therefore,  

TR = px ( 34 - 0.20x).x

= 34x - 0.2x²

For maximum TR -  

d(TR)/dx = 34 - 0.4x = 0

or x = 34/0.4  

= 85

Answer: The number of dozens in an order is 85.