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.