Question

1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+ r3 2 3 to the set of constraints for this problem? 2. Consider the linear programming problem and its final tableau from Question 1 (a) (2 points) Determine the range of change for the coefficient c3. That is, determine the interval within which c can change so that the given optimal solution remains optimal. (b) (2 points) Similarly, determine the range of change for 2 2. (c) (2 points) How can you change c3 so that the solution remains optimal? 3. Consider the following production problem Maximize z 10 12r2 +20r3 subject to the constraints 1 +22+3r3 22 2r1 22 4r3 K 30, 120, 20, 3 2 0 (a) (2 points) Solve the problem using the simplex method. Hint: Check your final tableau very carefully as the next parts will depend on its correct- ness. You end up having 1, 2,3 as basic variables. (b) (6 points) For 1,2, and 3, determine the admissible range for the variation of bi (denoted by Abi) so that the solution in Part (a) remains feasible Note: The entries of the solution will change, but the same variables have to remain basic.

Answer 1

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