Question 1

Answer the following questions using the sensitivity report shown below.

a) Report the optimal solution and the objective function. what is the range of

optimality for coefficient of x? (4 marks)

b) Report the range of feasibility associated with each constraint and Explain what

constraints are binding and which one(s) are non-binding. (5 marks)

c) Will the optimal solution remain optimal if the coefficient of x changes to 6? Explain

(1 marks)

d) If the coefficient of x changes to 5 and the coefficient of y changes to 3

simultaneously, will the optimal solution remain optimal? Explain (4 marks)

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

Type A x 10 0 3 8 1

Type B y 5 0 5 2 5

Type C z 0 -6.5 2 6.5 1E+30

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

Wood 1 15 1 15 20 10

Steel 2 30 1.5 30 110 30

hours 3 15 0 70 1E+30 5

Question 2

Answer the following questions using the sensitivity report shown below. a) Report the optimal solution and the objective function. what is the range of optimality for coefficient of x? (4 marks) b) Report the range of feasibility associated with each constraint and Explain what constraints are binding and which one(s) are non-binding. (5 marks) c) Will the optimal solution remain optimal if the coefficient of x changes to 7? Explain (1 marks) d). If the coefficient of x changes to 2 and the coefficient of y changes to 6 simultaneously, will the optimal solution remain optimal? Explain (4 marks) Variable Cells Final Reduced Objective Allowable Allowable Cell Name ValueCost Coefficient Increase Decrease Type Ax 10 0 8 Type By 5 0 2 Type Cz 0 1-6.5 6.5 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease Wood 1 15 15 20 10 Steel 2 30 1.5 30 110 30 hours 3 15 0 70 IE+30 553.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming problem that satises the optimality criterion. but is infeasible. Use the dual simplex method to restore feasibility. 1. 8. Use the dual simplex method to find a solution to the linear programming problem formed by adding the constraint 3x, + 5x3 2 15 to the problem in Example 2.Answer the following questions using the sensitivity report shown below. a) Report the optimal solution and the objective function. what is the range of optimality for coefficient of x? (4 marks) b) Report the range of feasibility associated with each constraint and Explain what constraints are binding and which one(s) are non-binding. (5 marks) c) Will the optimal solution remain optimal if the coefficient of x changes to 6? Explain (1 marks) d) If the coefficient of x changes to 5 and the coefficient of y changes to 3 simultaneously, will the optimal solution remain optimal? Explain (4 marks) Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease Type A 10 3 8 Type B 5 0 5 2 Type C z 6.5 65 16+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease Wood 15 15 20 10 Steel 30 15 30 110 30 hours 15 70 1E+30 55