Test Problem to be solved manually)

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(30 Minutes online Test Problem to be solved manually) (20 POINTS)

 

Consider the following linear programming problem:

 

          Minimize                       Z = 5x1 + 2x2

            Subject to

                                   3x1 +  6x2     ³ 18          I

5x1  + 4x2    ³ 20               II

                     8x1  + 2x2    > 16          III

                     7x1  + 6x2    £ 42          IV

                      x1,     x2    ³ 0

The following is a plot of the equality constraint

Write down the answers to questions (a to f) below:

 

  1. Shade the feasible region and indicate the optimal corner as P1.                           (1-points)

 

 

 

  1. What are the binding constraints in the given problem? Write the constraints numbers.(2-points)

 

 

 

 

 

 

  1. Solve the appropriate equations to find the optimal answer for the above problem. Show your solution and Summarize the answers below:            (7 points)

 

x1= _____;           x2=______; Z = _______.

 

 

 

 

S1= _____;               S2= _______;

 

 

 

 

S3= ______;              S4= _____;

 

 

               

Note: S1 to S4 are slack/surplus associated with constraints I to IV

 

 

 

  1. If the objective function in the above problem is changed to Maximize Z = 2x1 + 5x2, on the same graph above indicate the new optimal corner as P2:                                             (1-points)

 

 

 

 

 

  1. What are the binding constraints in the new modified problem? Write the constraints numbers.    (2-Point)

 

 

        

 

 

  1. Solve the appropriate equations to find the optimal answer for the new problem. Show you solution and summarize the answers below:          (7 points)

 

x1= _____;         x2=______;         Z = _______.

 

 

 

 

SP1= ____;                        SP2= _______;

 

 

 

 

SP3= ______;                      SP4= _____;

 

 

 

 

Note: SP1 to SP4 are the shadow prices associated with constraints I to IV