Maximize $Z = 2X_1 + 5X_2$

Subject to $X_1 + 4X_2 ≤ 24 \\ 3X_1 + X_2 ≤ 21 \\ X_1 + X_2 ≤ 9 \\ X_1, X_2 ≥ 0$

Mumbai University > MECH > Sem 7 > Operations Research

Marks: 10 M

Year: May 2014

Introducing surplus variables in the constraints:

$X_1 + 4X_2 ≤ 24 → X_1 + 4X_2 + S_1 = 24 \\ 3X_1 + X_2 ≤ 21 → 3X_1 + X_2 + S_2 = 21 \\ X_1 + X_2 ≤ 9 → X_1 + X_2 + S_3 = 9$

Maximization function becomes: $Z = 2X_1 + 5X_2 + 0S_1+ 0S_2+ 0S_3$

Iteration ends here.

$Z_{\max} = 33; X_1 =4; X_2 = 5$