1. A linear programming model is given as follows: Maximize z = 20x1 + 47x2 Subject to 50x1 + 24x2 1200 77x1 50x2 > 300 3x1 > 50 X1, x2 > 0 (a) Solve the problem by using the computer. What are the maximum Z and the optimal point? (b) Obtain the values of the slack/surplus variables at the optimal solution in (a) (c) Identify the sensitivity range of the objective function coefficient of X1. (d) Identify the sensitivity range of the value of the 1st resource constraint (right-hand side). (e) Identify the sensitivity range of the value of the 2nd resource constraint (right-hand side). (f) which of the following makes the model infeasible? (Choose one) i. Increase of the coefficient of x1 on the objective function to 3000 ii. Decrease of the coefficient of X1 on the 2nd constraint to -5000 Addition of a new constraint, x2 > 50 iv. Removal of the non-negativity constraints for X1, X2 None