Question 1 Consider the following tableau for a profit maximization linear programming (LP) problem where X1, X2, and X3 are the number of products to be manufactured and S1, S2 and S3 are non-negative slack variables associated with the first, second and third resources respectively. It is given that the objective function is Z = 10X +12X+14X3. Basic X2 X3 S S2 S3 RHS X1 -1 0 1 0 10 S2 0 2.5 0 -1.5 1 20 X3 0 1.5 1 -0.5 0 40 Z 0 -1 0 3 0 4 660 (a) What are the optimal solution and optimal objective value according to the above simplex tableau? (7 marks) 1 0.4 0.4 -0.6 2 1 2 (b) Given that -0.6 0.4 0.4 = 22 1 0.4 -0.6 0.4 22 Determine the original linear programming (LP) problem. (c) Determine the range of optimality for the objective coefficient of X2. (6 marks) (4 marks) (d) What is the dual price for the third resource? State the corresponding range of feasibility for the dual price. (4 marks) (e) If the objective coefficient of X2 changed to 13, what is the new optimal solution and the new optimal objective value? (4 marks)