Question: For the linear program: Max 3A + 4B s.t. A + 2B 8 Constraint 1 A + 2B 12 Constraint 2 2A + B 16

For the linear program:

Max 3A + 4B

s.t.

A + 2B 8 Constraint 1

A + 2B 12 Constraint 2

2A + B 16 Constraint 3

A, B 0

Should be done manually (must show hand work).

  1. Making A as the horizontal variable, graph the problem neatly. Show the feasible region. Label constraints on graphs.
  2. Solve the problem. Show work. What is the optimal A and B values? What is the optimal objective function value?
  3. What are the values of slack and surplus for each constraint?
  4. Holding the coefficient of B in the objective function fixed, how much can the coefficient of A decrease or increase so that the optimal solution does not change?
  5. Holding the coefficient of A in the objective function fixed, how much can the coefficient of B decrease or increase so that the optimal solution does not change?
  6. Suppose the coefficient of A changes from 3 to 5 and the coefficient of B changes from 4 to 2. Will the optimal solution change? If so, what is the new optimal solution?
  7. Which constraints have non-zero shadow prices? Explain.

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