Question

Find the solution to the following linear programming problem (if it exists) graphically: 

Maximize \( Z = x + y \) 
Subject to the constraints \[ x - y \leq -1, \quad -x + y \leq 0, \quad x, y \geq 0. \]

Hint:

For graphical LPP problems, plot the constraints, identify the feasible region, and evaluate the objective function at the vertices.

Answer 1

Step 1: Plot the constraints on the graph: \[ x - y = -1 \quad \Rightarrow \quad y = x + 1, \quad -x + y = 0 \quad \Rightarrow \quad y = x. \] 
Step 2: Identify the feasible region satisfying \( x, y \geq 0 \) and the constraints.
Step 3: Compute \( Z = x + y \) at each vertex of the feasible region. The maximum \( Z \) is the solution.