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(i) Show that x = (2,1,1) is a feasible point and label each of the constraints as binding (active) or non-binding (inactive). (Do not forget the non-negativity constraints) (ii) Find the set of all feasible directions p = (P1, P2, P3) at x. (iii) p=(-1,-1,-1) is a feasible direction. Determine the maximal step a > 0 such that x+op remains feasible.

(i) Show that x = (2,1,1) is a feasible point and label each of the constraints as binding (active) or non-binding (inactive). (Do not forget the non-negativity constraints) (ii) Find the set of all feasible directions p = (P1, P2, P3) at x. (iii) p=(-1,-1,-1) is a feasible direction. Determine the maximal step a > 0 such that x+op remains feasible.

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 linear programming problem z = 10z1 - 2T2 + 5x3 I1 + 12 – 2r3 >1 2x1 + 13 24 minimize subject to -I2+ 13 > 0 E1, 12, 13 20 (2, 1, 1)" is a feasible point and label each of the constraints as binding (active) or (1) Show that x = non-binding (inactive). (Do not forget the non-negativity constraints) (ii) Find the set of all fensible directions p = (Pi, P2, P3)" at x. (iii) p= (-1,-1,-1)" is a feasible direction. Determine the maximal step a > 0 such that x+ap remains feasible.
Transcribed Image Text:Consider the linear programming problem z = 10z1 - 2T2 + 5x3 I1 + 12 – 2r3 >1 2x1 + 13 24 minimize subject to -I2+ 13 > 0 E1, 12, 13 20 (2, 1, 1)" is a feasible point and label each of the constraints as binding (active) or (1) Show that x = non-binding (inactive). (Do not forget the non-negativity constraints) (ii) Find the set of all fensible directions p = (Pi, P2, P3)" at x. (iii) p= (-1,-1,-1)" is a feasible direction. Determine the maximal step a > 0 such that x+ap remains feasible.
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