Question

Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the objective? [2 marksJ b) What is the entering variable for the next step of the Revised Simplex Algorithm? [1 mark] c) What is the leaving variable? [1 mark] d) What is the new value of the objective? Verify that the new solution is optimal [2 marks] e) If the right-hand side of the third constraint is changed to 48 + δ for some value of δ > 0, what will happen to the value ofz? 12 marks/ f) Assuming no other data changes, what value does the objective function coefficient ofX1 have to reduce to so that, is zero in the optimal solution? [2 marks] Hint The following information may be useful 0 8 12 1 0 15 0l0 15 3 00 1 0 15 8L0 0 1 4 15 0 12 1 0 15 0 oll1 4 0 15 0 0 1 0 0

Answer 1

12o 12 Vari able 72- B O 67 3s(68 0 ne 2.