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To solve the given Linear Programming Problem (LPP) using the graphical method, we'll follow these steps: ### Problem Statement: Maximize: \[ z = 2x_1 + 3x_2 \] Subject to the constraints: \[ x_1 + x_2 \leq 4 \] \[ 2x_1 + x_2 \leq 5 \] \[ x_1, x_2 \geq 0 \] ### Step 1: Plot the Constraints First, we'll plot each constraint on the \( x_1 \)-\( x_2 \) plane. 1. Constraint 1: \( x_1 + x_2 \leq 4 \) - When \( x_1 = 0 \), \( x_2 = 4 \). - When \( x_2 = 0 \), \( x_1 = 4 \). - Plot the line connecting these two points. 2. Constraint 2: \( 2x_1 + x_2 \leq ______ ____ ________ __________ __________ ______ ________.
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