# What is the maximum value of #Q(p,q,r)=2pq+2pr+2qr# subject to #p+q+r=1#?

##### 2 Answers

Apr 7, 2018

#### Answer:

The maximum value of

#### Explanation:

We want to maximise

Let

#gradQ=lambdagradP#

#rArr((2q+2r),(2p+2r),(2p+2q))=lambda((1),(1),(1))#

So

Since

So the maximum value of

Apr 7, 2018

#### Answer:

See below.

#### Explanation:

The solution is at the tangency points between the sphere

with the plane

This point is for