Maximize $Z = 1000X_1 + 4000X_2 + 5000X_3$

Subject to $3X_1 + 3X_3 ≤ 22 \\ X_1 + 2X_2 + 3X_3 ≤ 20 \\ 3X_1 + 2X_2 ≤ 10 \\ X_1, X_2, X_3 ≥ 0$

Mumbai University > MECH > Sem 7 > Operations Research

Marks: 10 M

Year: May 12

Introducing slack variables in the constraints:

$3X_1 + 3X_3 ≤ 22 → 3X_1 + 3X_3+ S_1 = 22$

$X_1 + 2X_2 + 3X_3 ≤ 20 → X_1 + 2X_2 + 3X_3+ S_2 = 20$

$3X_1 + 2X_2 ≤ 10 → 3X_1 + 2X_2+ S_3 = 10$

Objective function becomes: $Z = 1000X_1 + 4000X_2 + 5000X_3 + 0S_1+ 0S_2+ 0S_3$

$X_2 = 5, X_3= \frac{10}{3} ; Max. Z = \dfrac{110000}{3}$