Consider the set X E R? defined by the system of inequalities X = {R² : -x1+ x2 < 2, x1 + x2 < 5, 2x1 + x2 < 4, x1 > 0, x2 > 0}. (a) In the two-dimensional coordinate system (x1, x2), clearly draw the set X. You may use the attached graph paper. (b) List all extreme points and their coordinates. Given the feasible set you graphed in problem 1, consider the following LP: minimize z(x1, x2) = -2x1 – x2 subject to = (x1, x2) E X. x = (a) Use the graphical method to find the set X* of all optimal solutions to this LP. Write this set using proper mathematical notation and provide the optimal objective value. (b) What is the value of the level curve of the objective function passing through the optimal solution?

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Hello, need help with the second part of this question, starting with "given the feasible set you graphed in problem 1". Thanks!

Consider the set X e R? defined by the system of inequalities
X = {R² : -x + x2 < 2, x1 + x2 < 5, 2x1 + x2 < 4, x1 > 0, x2 > 0}.
(a) In the two-dimensional coordinate system (x1, x2), clearly draw the set
X. You may use the attached graph paper.
(b) List all extreme points and their coordinates.
Given the feasible set you graphed in problem 1, consider the following LP:
minimize z(x1, x2) = –2x1 – X2
subject to
= (x1, X2) E X.
(a) Use the graphical method to find the set X* of all optimal solutions
to this LP. Write this set using proper mathematical notation and provide the
optimal objective value.
(b) What is the value of the level curve of the objective function passing
through the optimal solution?
Transcribed Image Text:Consider the set X e R? defined by the system of inequalities X = {R² : -x + x2 < 2, x1 + x2 < 5, 2x1 + x2 < 4, x1 > 0, x2 > 0}. (a) In the two-dimensional coordinate system (x1, x2), clearly draw the set X. You may use the attached graph paper. (b) List all extreme points and their coordinates. Given the feasible set you graphed in problem 1, consider the following LP: minimize z(x1, x2) = –2x1 – X2 subject to = (x1, X2) E X. (a) Use the graphical method to find the set X* of all optimal solutions to this LP. Write this set using proper mathematical notation and provide the optimal objective value. (b) What is the value of the level curve of the objective function passing through the optimal solution?
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