Question

"Use the graphical method to solve this problem:

Minimize Z = 15 X_1 + 20 X_2
Subject to X_1 + 2 X_2 ≥ 10
2X_1 – 3X_2 ≤ 6
X_1 + X_2 ≥ 6
and X_1 ≥ 0, X_2 ≥ 0"

Answer 1

(X_1, X_2) = (2, 4)

Z = 110

Explanation:

You want a graphical solution to ...

minimize Z = 15 X_1 +20 X_2

subject to ...

• X_1 + 2 X_2 ≥ 10
• 2X_1 – 3X_2 ≤ 6
• X_1 + X_2 ≥ 6
• X_1 ≥ 0
• X_2 ≥ 0

Graph

A graph of the reverse of the inequalities is attached. This makes the feasible solution region be white (rather than shaded multiple times), so its vertices are easier to see. (The dashed lines are part of the solution space.)

The vertex of the solution space that minimized the objective function is (X_1, X_2) = (2, 4). The minimum value of Z is 110.