Maximizing problem with an inequality constraint.

[Rabolisk]

Hello I have a worked example where I have to maximize a function with an inequality constraint. The problem is worked out below.

https://zgqqmw.sn2.livefilestore.com/y1pLc13HVWpA9dATZEzikySeSMBN2hn1mJCw71rJ5vvUJcr9W7KBPFkOz7HQEppa6EPbLi5yyAwDagh3ezF_7eyVL6tBK7q6ise/maxProbem.png?psid=1

I know how to get the kuhn-tucker conditions in the first step. I also understand how the first two possibilities (i) and (ii) are ruled out. In the third one the value of \lambda is 2. But how did the problem work out the value of and x₂ to be 10?

Thanks.

 

[algebrat]

In case (iii), x_1=0. Why not just go back to the original conditions, you are trying to maximize y=2*x_2 subject to the constraint x_2<=10, so clearly we have a max when x_2=10, thus y=20.