UNIVERSITY OF MANCHESTER
20 January 2009
Answer THREE questions from Four
Electronic calculators may be used, provided that they cannot store text.
1 of 5 P.T.O.
1. Define the terms (i) basic feasible solution, and (ii) extreme point (of the feasible region) for
a linear programming (LP) problem with n variables and m constraints in standard form.
Explain how they are related and state the fundamental theorem of linear programming.
Consider the following LP
Minimize 3x1 + x2 + 2x3
subject to x1 + x2 - 2x3 1
x1 - 2x2 + x3 -1
x1, x2, x3 0.
(a) Express this LP in standard form, state the Phase I problem and solve by the Two Phase