Find the optimum solution to the following LP by using the
Simplex Algorithm.
Min z = 3x1 – 2x2+ 3x3
s.t.
-x1 + 3x2 ≤ 3
x1 + 2x2 ≤ 6
x1, x2, x3≥ 0
a) Convert the LP into a maximization problem in standard
form.
b) Construct the initial tableau and find a bfs.
c) Apply the Simplex Algorithm.
Find the optimum solution to the following LP using the Simplex
Algorithm. Use Two-Phase method.
??? ?=3?2+2?3 ??
−2?1 + ?2 − ?3 ≤ −3
−?1 + 2?2 + ?3 = 6
?1,?2,?3 ≥0
Find the optimum solution to the following LP using the Simplex
Algorithm. Use Big M method.
??? ?=5?1+2?2+?3 ??
?1 + ?2 ≤ 6
?1 − ?2 + 2?3 ≤ 2
3?1 + 2?2 = 12
?1,?2,?3 ≥0
Consider the following LP. Use revised simplex formula to
answer the questions.
Max Z = -x1 +2x3 +3x4
subject to
x1 -x2+2x3 ≥8
4x1 +2x2 +7x3 +9x4 ≥ 30 2x1 +3x3 +7x4 ≤ 20 3x1 +x2 -3x3 +4x4 =
1 x1, x2, x3, x4 ≥ 0
a. Show that the basic feasible solution where x1, x2, x3, and
x4 is not a feasible solution to the given LP.
b. Show that the basic feasible solution where x1, x3, x4, and...
Use the simplex method to solve the linear programming
problem.
Maximize objective function: Z= 6x1 + 2x2
Subject to constraints:
3x1 + 2x2 <=9
x1 + 3x2 <= 5
when x1, x2 >=0