Question 1 (20 Marks) Consider the following linear programming problem Maximize 10x+9x2 Subject to: Tox2 + 1x2 5 630 1 5 ZX1 + 5x2 -X1 + X2 5600 2 1x: +3*2 = 708 Tox tix s 135 X1, X2 20 The final simplex tableau can be referred to Table 1. Table 1: Final simplex tableau for LPP Question 1. X1 10 X2 9 $2 0 S4 0 Basis SI 0 30 16 S3 0 21 16 X2 9 0 0 0 252 15 S2 0 0 0 0 120 16 20 5 32 30 16 X] 10 0 0 0 540 $4 0 0 0 16 11 32 70 0 9 64 18 10 9 0 111 16 0 7668 C-2 0 0 70 16 0 111 16 0 a. What is the range of optimality for the objective function coefficient x;? [3 marks) b. What is the range of optimality for the objective function coefficient x?? [3 marks] c. How will the optimal solution above be affected if the coefficient of x2 changed from 9 to 7? [5 marks] d. Calculate the range of feasibility for b, ba, b; and bt. [3 marks] e. What is the increase that can happen to the optimal solution if b, were increased from 630 to 660? [3 marks] f. What is the decrease that can happen to the optimal solution if the resources (right-hand side) of the second constraint reduced by 40? [3 marks]