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Consider the following system of linear inequalities who set of simultaneous solutions defines a convex region: T1 – X2 > -4 4.x1 +5x2 < 40 5x – 2x2 < 20 5x1 + 2x2 > 10 T1, T2 > 0 (a) Convert the first four inequalities to equalities using nonnegative slack variables. (b) What is an upper bound on the number of basic solutions for this system? Explain.

Consider the following system of linear inequalities who set of simultaneous solutions defines a convex region: T1 – X2 > -4 4.x1 +5x2 < 40 5x – 2x2 < 20 5x1 + 2x2 > 10 T1, T2 > 0 (a) Convert the first four inequalities to equalities using nonnegative slack variables. (b) What is an upper bound on the number of basic solutions for this system? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following system of linear inequalities who set of simultaneous solutions defines a convex region: X1 – X2 > -4 4.r1 + 5x2 < 40 5x1 - 2x, < 20 5x1 + 2x2 > 10 21, T2 > 0 (a) Convert the first four inequalities to equalities using nonnegative slack variables. (b) What is an upper bound on the number of basic solutions for this system? Explain. (c) Find all basic solutions for this LP. (You may use a computer to assist in the calcu- lations.) For each basic solution, specify which variables are basic and which are nonbasic. Which of the basic solutions are basic feasible solutions?
Transcribed Image Text:Consider the following system of linear inequalities who set of simultaneous solutions defines a convex region: X1 – X2 > -4 4.r1 + 5x2 < 40 5x1 - 2x, < 20 5x1 + 2x2 > 10 21, T2 > 0 (a) Convert the first four inequalities to equalities using nonnegative slack variables. (b) What is an upper bound on the number of basic solutions for this system? Explain. (c) Find all basic solutions for this LP. (You may use a computer to assist in the calcu- lations.) For each basic solution, specify which variables are basic and which are nonbasic. Which of the basic solutions are basic feasible solutions?
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