Find the maximum and minimum values of the function $ z = 2x - y $ subject to the constraints:\[ x + y \leq 4 \]\[ x \geq 0 \]\[ y \geq 0 \]

Answered: Find the maximum and minimum values z =…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.8: Linear And Quadratic Functions

Problem 4ST

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Question

Find the maximum and minimum values of the function $ z = 2x - y $ subject to the constraints:

\[ x + y \leq 4 \]

\[ x \geq 0 \]

\[ y \geq 0 \]

Expert Solution

Step 1

A scalar function $f (x, y)$ is a rule that is used to associate a number or quantity with a particular point $(x, y)$ in space. In this problem, the multivariable function is $z = 2 x - y$ , we have to find its maximum and minimum, subject to the constraints $x + y \leq 4, x \geq 0$ and $y \geq 0$ .