# Functions: K-T Condition

Not what you're looking for?

Consider the following program:

Maximize f(x,y)=x^2+4xy+y^2

subject to g(x,y)=x^2+y^2-1=0

##### Purchase this Solution

##### Solution Summary

A function is maximized using Kuhn-Tucker condition. The maximized function results are determined.

##### Solution Preview

Solution. Let us denote the gradient vector of the function f(x,y) by Df(x,y). We rewrite the original program as follows.

Minimize F(x,y)=-f(x,y)=-x^2-4xy-y^2

. g(x,y)=x^2+y^2-1=0.

Since DF(x,y)=(-2x-4y,-4x-2y)', Dg(x,y)=(2x,2y)', by K-T ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.