Maximize $Z = 3X_1 + 5X_2$

Subject to $X_1 ≤ 4 \\ X_2 ≤ 6 \\ 3X_1 + 2X_2 ≤ 18 \\ X_1, X_2 ≥ 0$

• Stage I:

  $F_1$ $= Maximize 3X_1 \\ = 3 \max. (X_1)$

  From the constraints:

  $X_1 ≤ 4 \\ 3X_1 + 2X_2 ≤ 18→X_1 ≤ \dfrac{18 - 2X_2}{3}$

  So $X_1 ≤ \min. \bigg[4,\dfrac{18 - 2X_2}{3}\bigg]$

  Therefore, $F_1 = 3 \min. \bigg[4, \dfrac{18 - 2X_2}{3} \bigg]$

  The maximum value that $X_1$ can …