MTH601 Quiz Solution by Aziz Raaj

MTH 601 Assignment Solution Sector In charge : Saima kanwal

Q1. Solve the program using M-method.

Minimize · Z=2x1+3x2 · 0.5 x1+0.25 x2≤4 · x1+3 x2≥20 · x1+ x2=10 · x1, x2≥0 · Solution:

To solve the given linear programming problem using the M-method, we need to convert the inequalities into equations and introduce slack, surplus, and artificial variables.

Let's rewrite the problem with slack variables:

Minimize: Z = 2x1 + 3x2

1. 5x1 + 0.25x2 + s1 = 4

(Equation 1):

x1 + 3x2 – s2 = 20

(Equation 2):

X1 + x2 + s3 = 10

(Equation 3):

X1, x2, s1, s2, s3 ≥0 Now, we introduce artificial variables and a big-M value to convert the inequalities into equations: