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The given Linear Programming Problem (LPP) is: Maximize ( z = 10x_1 + 10x_2 ) subject to: [ 4x_1 + 3x_2 \le 12, \quad 6x_1 + 18x_2 \le 36, \quad x_1, x_2 \ge 0 ] First, we convert the inequalities to equalities to find the boundary lines: 1. ( 4x_1 + 3x_2 = 12 ) * (x_1)-intercept: (x_2 = 0 \Rightarrow 4x_1 = 12 \Rightarrow x_1 = 3) * (x_2)-intercept: (x_1 = 0 \Rightarrow 3x_2 = 12 \Rightarrow x_2 = 4) 2. ( 6x_1 + 18x_2 = 36 ) * (x_1)-intercept: (x_2 = 0 \Rightarrow 6x_1 = 36 \Rightarrow x_1 = ______ ________ _____ ____ _______ ______ ____.
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