Question: (40 points) Consider the following linear program: Minimize 3 X 1 +7 X 2 50 X 1 +100 X 2 100,000 5 X 1 +4

  1. (40 points) Consider the following linear program:

Minimize 3X1+7X2

50X1+100X2100,000

5X1+4X26,000

4X1+10X25,000

  1. Find the common feasible region
  2. Find the solution (Hint: the total of the objective function should be 3735.294).
  3. Find the range of C1C2 only
  4. Using your answer to question (3) if the objective function coefficient of X1 increases to 7, what will happen?
  5. Using your answer to question (3) if the objective function coefficient of X2 falls to 3, what will happen?
  6. Using your answer to question (3) if the objective function coefficient of X1 rises to 10, and the objective function coefficient of X2 rises also to 10, what will happen?
  7. Find the ranges of optimality.
  8. If the objective function coefficient of X1 rises to 30, and the objective function coefficient of X2 rises to 60 apply the revised 100% rule. Check your answer against your answer to question (3). What do you notice?

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