Q. 5 Describe two methods for optimiz... [FREE SOLUTION]

Chapter 12: Q. 5 (page 985)

Describe two methods for optimizing a function $z = f (x, y)$ subject to a constraint.

Short Answer

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The first method to optimize a function is, by using the derivative method. The second method to optimize a function is, by using Lagrange multipliers.

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Step 1. Given information

We need to explain the two methods for optimizing a function $z = f (x, y)$ subject to a constraint.

Step 2.The two methods for optimizing a function z=fx,y subject to a constraint.

To optimize a function of two variables $z = f (x, y)$ subjected to a constraint $g (x, y) = 0$ one way is to solve $g (x, y) = 0$ in terms of $x$ or $y$ and use that value in $f (x, y)$ so that $f (x, y)$ becomes a function of one variable only, then using the derivative method the extreme value can be found out.

The second method is, to use the Lagrange multipliers in which a scalar $位$ is multiplied to the constraint $g (x, y) = 0$ and then the equation $鈭� f (x, y) = 位鈭� g (x, y)$ is solved to find the points where the function can have extreme value.

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91影视

Describe two methods for optimizing a function $z = f (x, y)$ subject to a constraint.

Short Answer

Step by step solution

Step 1. Given information

Step 2.The two methods for optimizing a function z=fx,y subject to a constraint.

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91影视

Describe two methods for optimizing a function z=f(x,y)subject to a constraint.

Short Answer

Step by step solution

Step 1. Given information

Step 2.The two methods for optimizing a function z=fx,y subject to a constraint.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Describe two methods for optimizing a function $z = f (x, y)$ subject to a constraint.