Question: 3. (10 pts.) Consider an LP with the optimal simplex tableau shown below: Z X1 RHS 1 X2 0 0 X4 2 0 X3 0

3. (10 pts.) Consider an LP with the optimal

3. (10 pts.) Consider an LP with the optimal simplex tableau shown below: Z X1 RHS 1 X2 0 0 X4 2 0 X3 0 -1 2 2 0 1 1 3 0 0 1 -2 3 a) Does this LP have more than one bfs that is optimal? b) How many optimal solutions does this LP have? (Hint: If the value of xz is increased, then how does this change the values of the basic variables and the z-value?) 4. (20 pts.) Consider the following problem. min Z = 3x1 + 8x2 + 5x3 St. 3x2 + 4x3 > 70 3x1 + 5x2 + 2x3 70 X1, X2 X3 > 0 Using the Big M method, work through the simplex algorithm step by step to solve the problem. Verify your answer using a software package (LINDO/LINGO). (You do not need to submit the output for your software package.)

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