5) Answer the following questions using the sensitivity report shown below (10 min) 15 marks a) Report the optimal solution and the objective function. what is the range of optimality for coefficient of y? (6 marks) b) Calculate the amount of slack or surplus for each constraint and comment on whether it is slack or surplus (4 marks) Variable Cells Final Reduced Objective Allowable Allowable c) Assuming Wood cost to be Cell Name Value Cost Coefficient increase Decre.se Type Ax 9 sunk, how much should the Type By company pay for additional 25 Type CZ units of wood? (5 marks) 0 3 0 3 S 2 6 3 6.5 2 4 1E430 -6.5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease Wood 1 25 1 25 20 10 Steel 2 30 0 40 1E+30 30 hours 55 3 -1.5 65 72 35 Nm 5) Answer the following questions using the sensitivity report shown below (15 min) 15 marks d) Interpret the reduced cost of -6.5 for the variable "z". (4 marks) e) If the coefficient of x changes to 7 and the coefficient of y changes to 4 simultaneously, will the optimal solution remain optimal? Explain (6 marks) Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost coefficient Increase Decre.se Type Ax 9 0 3 6 2 Type By 3 0 5 3 Type C z 0 -6.5 2 6.5 1E+30 f) How much improvement is expected in the objective function if we reduce the number of available hours from 55 to 25? (5 marks) 4 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease Wood 1 25 1 25 20 10 Steel 2 30 0 40 1E+30 30 hours 3 55 -1.5 55 72 35