Problem Statement
Solve graphically: Maximize and Minimize $Z = 5x + 10y$ subject to $x + 2y \le 120$, $x + y \ge 60$, $x - 2y \ge 0$, and $x, y \ge 0$.
Verified Solution & Marking Scheme
Identify Corner Points
Intersection of lines gives vertices: $A(40, 20)$, $B(60, 30)$, $C(120, 0)$, $D(60, 0)$.
Evaluate Objective Function
$Z(A) = 400$, $Z(B) = 600$, $Z(C) = 600$, $Z(D) = 300$.
State Maximum and Minimum
Max $Z = 600$ at all points on line segment $BC$; Min $Z = 300$ at $(60, 0)$.