1.

The sum of two natural numbers is 48. Find the numbers when their product is maximum. 

Answer»

Let the two numbers be x & y. 

Given x + y = 48 & product: = xy where y 48 – x. 

Let p = xy = x (48 – x) 

dp/dx = 48x – x2

dp/dx = 48 – 2x 

dp/dx = 0 ⇒ 48 – 2x = 0 x = 24 

d2p/dx2= -2 < 0 ⇒ product is maximum 

x = 24 ⇒ y = 48 – 24 = 24 

⇒ the two numbers are 24, 24.



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