[solved]-Problem 3 03 Consider Following Linear Program Min 8x 12y St 1x 3y 9 2x 2y 10 6x 2y 18 X Y Q39669253

Problem 3-03

Consider the following linear program:

Min8X + 12Ys.t.1X + 3Y ≥ 92X + 2Y ≥ 106X + 2Y ≥ 18  X, Y ≥ 0

1. Choose the correct graph which represents the optimalsolution.
   (i)(ii)(iii)(iv)
   Graph (iv)
2. Assume that the objective function coefficient for X changesfrom 8 to 6. Does the optimal solution change? Use the graphicalsolution procedure to find the new optimal solution. If required,round your answers to the nearest whole number.

   The same extreme point remains optimal
   XYOptimal solution

3. Assume that the objective function coefficient for X remains 8,but the objective function coefficient for Y changes from 12 to 6.Does the optimal solution change? Use the graphical solutionprocedure to find the new optimal solution. If required, round youranswers to the nearest whole number.

   A new extreme point becomes optimal
   XYOptimal solution

4. The computer solution for the linear program in part (a)provides the following objective coefficient rangeinformation:
   VariableObjective CoefficientAllowable IncreaseAllowable DecreaseX8.0004.0004.000Y12.00012.0004.000

   How would this objective coefficient range information help youanswer parts (b) and (c) prior to re-solving the problem?

   The objective coefficient range for variable X is  to .Since the change in part (b) is in  this range, we knowthat the optimal solution will not  change.

   The objective coefficient range for Y isfrom  to  so the optimalsolution   change in part (c) because the newobjective coefficient is not in  this range.

Expert Answer

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Answer to Problem 3-03 Consider the following linear program: Min 8X + 12Y s.t. 1X + 3Y ≥ 9 2X + 2Y ≥ 10 6X + 2Y ≥ 18 X, Y �… . . .