(45 marks) We are given the following algebraic model: maximize 4x1 + 9x2 subject to (1) 15x1 + 3x2 450 (2) 40x1 + 10x2 400 (3) 10x1 + 8x2 420 (4) 4x1 + 20x2 588 x1 , x2 0 (a) Solve the model graphically, using a 50 by 50 grid. (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.