acy ercise 3.16 (Lexicography and the revised simplex method) that we have a bas

Question

acy ercise 3.16 (Lexicography and the revised simplex method) that we have a basic feasible solution and an associated basis matrix B su every row of B-1 is lexicographically positive. Consider a pivoting rule that chooses the entering variable x, arbitrarily (as long as c 0) and the exiting variable as follows. Let u = B-1A,. For each i with ui > 0, divide the ith row of B b B-1] by ui and choose the row which is lexicographically smallest. If row t was lexicographically smallest, then the lth basic variable ag exits the basis. Prove the following: (a) The row vector (-c'g B-b,-cgB-1) increases lexicographically at each Suppose ch that iteration. (b) Every row of B1 is lexicographically positive throughout the algorithm. (c) The revised simplex method terminates after a finite number of steps.

Explanation / Answer

Answer:

(a) x1 will replace x3 in the basis. So new value of x1 will be equal to the value x3 had before.

(b) Numerical value of objective function = previous value + (?j x minimum ratio )

= previous value + ((c,j - ?T aj ) x minimum ratio)

= 75 + (-(-5) x 2) = 85

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.