Maximizing problem with an inequality constraint.

by Rabolisk
Tags: constraint, inequality, maximizing
Rabolisk is offline
Dec10-12, 11:57 AM
P: 6
Hello I have a worked example where I have to maximize a function with an inequality constraint. The problem is worked out below.

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 [itex]\lambda[/itex] is 2. But how did the problem work out the value of and x2 to be 10?

Attached Thumbnails
Phys.Org News Partner Science news on
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
algebrat is offline
Dec11-12, 01:31 AM
P: 428
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.

Register to reply

Related Discussions
Maximizing a multivariate function under a constraint Calculus & Beyond Homework 3
optimization subject to inequality constraint Calculus & Beyond Homework 4
Newton's method with inequality constraint General Math 5
Lagrange multiplier with inequality and point constraint? Calculus & Beyond Homework 10
Optimization inequality constraint Calculus & Beyond Homework 4