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4. The following question examines the case of a linear program in which two basic feasible solutions B1 and B2 correspond to the same extreme point. a. Give an example of a linear program in standard form in which two different non-optimal basic feasible solutions B1 and B2 correspond to the same extreme point w. b. Let q be the number of variables in this linear program, and let A1 and A2 be the set of columns corresponding to the non-zero variables in B1 and B2. i. Verify that the number of columns in A1 (A2) is less than q. ii. Show that the columns in A1 (A2) are linearly independent. iii. Add columns to A1 to form a basis corresponding to the extreme point w.

          4. The following question examines the case of a linear program in which two basic feasible solutions B1 and B2 correspond to the same extreme point.
a. Give an example of a linear program in standard form in which two different non-optimal basic feasible solutions B1 and B2 correspond to the same extreme point w.
b. Let q be the number of variables in this linear program, and let A1 and A2 be the set of columns corresponding to the non-zero variables in B1 and B2.
i. Verify that the number of columns in A1 (A2) is less than q.
ii. Show that the columns in A1 (A2) are linearly independent.
iii. Add columns to A1 to form a basis corresponding to the extreme point w.

4. The following question examines the case of a linear program in which two basic feasible solutions B1 and B2 correspond to the same extreme point.
a. Give an example of a linear program in standard form in which two different non-optimal basic feasible solutions B1 and B2 correspond to the same extreme point w.
b. Let q be the number of variables in this linear program, and let A1 and A2 be the set of columns corresponding to the non-zero variables in B1 and B2.
i. Verify that the number of columns in A1 (A2) is less than q.
ii. Show that the columns in A1 (A2) are linearly independent.
iii. Add columns to A1 to form a basis corresponding to the extreme point w.

Added by Ryan S.

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