 
Summary: MATH39011
Two hours
UNIVERSITY OF MANCHESTER
MATHEMATICAL PROGRAMMING
20 January 2009
09.45 11.45
Answer THREE questions from Four
Electronic calculators may be used, provided that they cannot store text.
1 of 5 P.T.O.
MATH39011
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.
[6 marks]
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
