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Consider the set of vectors S = (9, 6, −1), (1, −7, 3), (−6, 9, 5), (3, 1, 5). (a) Create a linear program that would determine if the vector (4, 1, 2) can be ex- pressed as a convex combination of the vectors in the set S. (You will need a “dummy” objective function like min 0.) (b) Try to solve your model from part (a) using Matlab’s linprog function (or other software). If the model is feasible, report your solution. If it is infeasible, report that fact. (c) Is (4, 1, 2) within the convex hull of S? Explain.

Consider the set of vectors S = (9, 6, −1), (1, −7, 3), (−6, 9, 5), (3, 1, 5). (a) Create a linear program that would determine if the vector (4, 1, 2) can be ex- pressed as a convex combination of the vectors in the set S. (You will need a “dummy” objective function like min 0.) (b) Try to solve your model from part (a) using Matlab’s linprog function (or other software). If the model is feasible, report your solution. If it is infeasible, report that fact. (c) Is (4, 1, 2) within the convex hull of S? Explain.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Consider the set of vectors S = (9, 6, −1), (1, −7, 3), (−6, 9, 5), (3, 1, 5).
(a) Create a linear program that would determine if the vector (4, 1, 2) can be ex-
pressed as a convex combination of the vectors in the set S. (You will need a
“dummy” objective function like min 0.)
(b) Try to solve your model from part (a) using Matlab’s linprog function (or other
software). If the model is feasible, report your solution. If it is infeasible, report
that fact.
(c) Is (4, 1, 2) within the convex hull of S? Explain.

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