2. (45 marks) We are given the following algebraic model: 4x1 + 9x2 maximize subject to...

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2. (45 marks) We are given the following algebraic model: 4x1 + 9x2 maximize subject to (1) (2) (3) 10x₁ + 8x2 < 420 (4) 4x₁ + 20x2 < 588 15x₁ + 3x2 < 450 40x₁10x2 2 400 x2 > (a) Solve the model graphically, using a 50 by 50 grid. 5 0 (b) Perform a sensitivity analysis for each of the objective function coefficients. (c) Perform a sensitivity analysis for the right-hand-side values for each of the non- binding constraints. (d) Find the AI (allowable increase) and AD (allowable decrease) for the righthand- side values for each of the two binding constraints. (e) For each of the two binding constraints, find the change to each variable as function of the right-hand side value, and from these relationships calculate the two shadow prices. 2. (45 marks) We are given the following algebraic model: 4x1 + 9x2 maximize subject to (1) (2) (3) 10x₁ + 8x2 < 420 (4) 4x₁ + 20x2 < 588 15x₁ + 3x2 < 450 40x₁10x2 2 400 x2 > (a) Solve the model graphically, using a 50 by 50 grid. 5 0 (b) Perform a sensitivity analysis for each of the objective function coefficients. (c) Perform a sensitivity analysis for the right-hand-side values for each of the non- binding constraints. (d) Find the AI (allowable increase) and AD (allowable decrease) for the righthand- side values for each of the two binding constraints. (e) For each of the two binding constraints, find the change to each variable as function of the right-hand side value, and from these relationships calculate the two shadow prices.