MAT 168 – Spring 2009
HW Set 3, Part 2 of 3 (Due Wed. April 22)
(H3P2.1) Consider the following linear program
min z=−x1−2x2
s.t.
x1+x2≤9
x1−x2≤3
x2≤5
x≥0
(i) Draw the feasible region in R2and determine the solution graphically.
(ii) Solve the problem by the Simplex Method using Tableaus. Trace in contrasting color
the path that the Simplex Method takes on your figure.
(H3P2.2) (i) Solve the following linear program by the Simplex Method
min z=−2x2−x3
s.t.
x1−x2≤3
x2−x3≤3
x≥0
(ii) Observe that the problem is unbounded. What is the current basis when the Ratio Test
fails to select the exiting variable? What is the corresponding basic feasible solution?
(iii) Find all linearly independent direction of unboundedness.
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