Question

Consider the following LP problem:           Max   3X1 + 2X2           s.t. 5X1 + 4X2 £...

Consider the following LP problem:

          Max   3X1 + 2X2

          s.t. 5X1 + 4X2 £ 40

                3X1 + 5X2 £ 30

                3X1 + 3X2 £ 30

                       2X2 £ 10

                X1 ³ 0, X2 ³ 0

(1)   Show each constraint and the feasible region by graphs. Indicate the feasible region clearly.   (5 points)

(2)   Are there any redundant constraints? If so, what constraint(s) is redundant? (2 points)

(3)   Identify the optimal point on your graph. What are the values of X1

      and X2 at the optimal point? What is the optimal value of the

      objective function? (5 points)

(4)   What would be the optimal values of X1 and X2 and the optimal value of the objective function if the objective function is changed to Max 3X1 + 9X2 while all constraints remain unchanged? (5 points)

(5)   Suppose there is one more constraint X1 => 10 in addition to the original problem. What is the optimal solution? (3 points)

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