Write the objective function in terms of non-basic variables

Question

Problem:

Operations Research: Simplex Tableau

Use the Simplex Tableau Method to solve the following linear programming problem.

Maximise          z=5x₁ + 3x₂
subject to:       4x₁ + 2x₂ <= 15
                        4x₁ + x₂ <= 10
                        x₁ + x₂ <=4
                        x_j >= 0, j =1,2.

Use the optimal tableau above to answer the following.

i) State the maximum value of z.

ii) State the values of all the basic variables at the optimal point.

iii) Write the objective function in terms of the non-basic variables.

iv) Write each of the basic variables in terms of the non-basic variables.

v) At the optimal point, which of the three constraints are active and which are inactive. Justify your answer.