Home
Class 12
PHYSICS
Divide 20 into two parts such that the p...

Divide 20 into two parts such that the product of one part and the cube of the other is maximum. The two parts are

A

`(10,10)`

B

`(5,15)`

C

`(13,7)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`x+y=20` and `z=xy^(3)`
`impliesz=y^(3)(20-y)=20y^(3)-y^(4)`
`implies(dz)/(dy)=60y^(2)-4y^(3)=0implies4y^(2)(15-y)=0`
So, either `y=0, or y=15`
Now `(d^(2)z)/(dy^(2))=120y-12y^(2),bacauseAt y=0, (d^(2)z)/(dy^(2))gt0`
`bacausey=0` is the point of minima and at `y=15,(d^(2)z)/(dy^(2))lt0`
`becausey=15` is the point of maximum.
Hence the required parts is `(5,15)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Divide 15 into two parts such that product of square of one part and cube of other is maximum

Divide the number 84 into two parts such that the product of one part and the square of other is maximum.

Divide 20 into two parts such that the product of the cube of one and the square of the other shall be maximum

What is the product of two parts of 20 such that the product of one part and the cube of the other is maximum?

20 is divided into two parts so that product of cube of one quantity and square of the other quantity is maximum. The parts are

Divide 8 into two positive parts such that the sum of the square of one and the cube of the other is minimum.

Divide 500 into two parts such that the ratio of one to the other are in 5 : 3?