Q4. (20 marks) If the objective function (Z [$k]) and results for the final iteration of the Simplex Method for an LP problem are as below: Iteration Final Basic Variables Z X1 X4 X2 Eq. Max Z = 3x + 5x N (0) 1 (1) (2) (3) 0 0 0 X1 0 1 0 0 Coefficients X 0 0 0 1 X3 3/2 3 1/5 3/4 X4 0 0 1 0 X5 c) Find feasibility ranges of change for all resources. d) Determine whether dual prices are binding constraints or not. Explain how these resulted. M+1 -4/3 e) Determine if resources are Free or Scarce goods. Explain how these resulted. -2 1 RHS 33 6 4 If all constraints are related to the available resources (kg), answer the following questions: a) What are Dual Prices (D)? Explain how they can be evaluated. b) How Dual Prices (D) can contribute to the objective function (Z)? Formulate their contribution and explain it in simple sentences. 3 (4 marks) (5 marks) (5 marks) (3 marks) (3 marks)

Q4. (20 marks) If the objective function ( Z[$k] ) and results for the final iteration of the Simplex Method for an LP problem are as below: MaxZ=3x1+5x2 If all constraints are related to the available resources (kg), answer the following questions: a) What are Dual Prices ( D1) ? Explain how they can be evaluated. (4 marks) b) How Dual Prices (Di) can contribute to the objective function (Z) ? (5 marks) Formulate their contribution and explain it in simple sentences. c) Find feasibility ranges of change for all resources. d) Determine whether dual prices are binding constraints or not. Explain how (5 marks) these resulted. (3 marks) e) Determine if resources are Free or Scarce goods. Explain how these resulted