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Consider this problem and answer the following questions. Maximize      Z = 2x1 + 3x2           s.t....

Consider this problem and answer the following questions.

Maximize      Z = 2x1 + 3x2

          s.t.

                               x1   +   2x2 <= 30

                               x1    +    x2   <= 20

                               x1,          x2   >= 0

  1. Solve the problem graphically in a free hand manner and identify all the CPFs.
  2. Use hand calculation to solve the problem by the simplex method in algebraic form
  3. Additional:
  1. What can you say about the solution if the RHS of the second constraint was 16? (i. e. b2 = 16), How about b2 = 14? What is the new solution? Also show these cases graphically.
  2. What if the RHS of the first constraint was 25? Does the solution change? if so, show how does it change?
  3. What if the coefficient of x1 in the objective function was 4? How does the solution change? Also show these cases graphically.
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