1. Choose a three-dimensional LP maximization problem (n = 3) with two constraints (m = 2) of your own choice. Solve the problem by using the Excel Solver. Change your problem if it does not have a feasible solution. Otherwise, generate the Solver Answer Report and record the number of simplex iterations and the computer execution time in that report. Remember to select Simplex LP as the Solver's solution method when solving the problem.

2. Add another constraint to the existing constraints of the problem that you have chosen (m = 3). Repeat the steps described in #1. You may change your problem whenever a feasible solution does not exist, but make sure that n = 3 and m = 3 in your problem.

3. Repeat the previous steps for n = 3 and successive m values of m = 4, 5, and 6 by successively adding a constraint to the current collection of constraints.

4. Plot the number of simplex iterations (y) versus the number of constraints (m). Save your plot as a picture file, and upload it in your discussion thread.

5. Plot the computer execution time (t) versus the number of constraints m. Save your plot as a picture file, and upload it in your discussion thread. (Use four significant places after the decimal for t.)

Describe how the number of constraints and the required number of simplex iterations are related, according to your observations. Is this relation linear? Polynomial? Rational? Exponential? Furthermore, how are the number of constraints and the computer execution time related? Is this relation linear? Polynomial? Rational? Exponential?