ARTIFICIAL STARTING SOLUTION (10 points each) 1. Consider the following set of constraints: X1 + x2 + x3 = 7 2x1 5x2 + x3 > 10 X1, X2, X3 20 (a) Maximize z = 2x1 3x2 - 5x3 (Use M-Method) (b) Minimize z = 2x1 3x2 5x3 (Use M-Method) (c) Maximize z = x1 + 2x2 + 4x3 (Use Two-Phase Method) (d) Minimize z = 4x1 - 6x2 + 3x3 (Use Two-Phase Method) 2. Consider the following LP (Use Two-Phase Method): Maximize z = 2x1 + 3x2 + 4x3 Subject to 2x1 + x2 + x3 = 2 3x1 + 4x2 + 2x3 = 8 X1, X2, X3 20 GRAPHICAL SENSITIVITY ANALYSIS (25 points) 1. For the following problem, use graphical sensitivity analysis to: a. Compute the optimality range of c1 assuming that c2 is constant. (5 points) b. Compute the unit worth of resource 1 (defined by first constraint) and its feasibility range (HINT: you can refer to section 3.6.1 of the textbook) (20 points). Maximize z = 4x1 + 2x2 Subject to 6x1 + 4x2