PLB Pty Ltd produces two products in three departments. Details are shown below regarding the time per unit required in each department, the available hours in each department and the contribution per unit of each product: Department A Department B Department C Contribution per unit Product X Hours per unit 8 4 12 R4/unit Product Y Hours per unit 10 10 6 R8/unit Available hours 11 000 9 000 12 000 NB: The optimal point in the feasible region is at point C where the constraints for Department A and B intersect. Required: 1.1 Use a linear programming graph and simultaneous equations to determine the optimal production plan for the three departments, Department A; B and C. Show all calculations. Do no draw a graph. (17) 1.2 Determine the slack for Department A; B and C. Indicate in your answer if there is slack or no slack. (6) 1.3 Calculate the shadow price if one extra hour is made available for each of the following departments: a. Department A b. Department B c. Department C NB: Round off cost per unit; hours; units and total costs to 2 decimal places. (3) (3) (1)