4. Karen is selecting courses for her graduate degree in operations research. The table below displays the available courses, the average weekly hours she expects to devote to each course, her minimum expected grade, and the number of credit hours. Course Introduction to Ops Research Linear Optimization Average Weekly Hours Minimum Grade Credits 3 6 Integer Optimization Nonlinear Optimization Modeling & Simulation Probability and Statistics Data Mining Scientific Computing Consider the following: 8 10 6 5 6 10 2 3 3 3 4 3 1 14 (a) Karen wants her expected grade point average to be at least 2.5. She will receives 4, 3, 2, and 1 points toward her GPA for grades of A, B, C, and D, respectively. (b) To remain a full time student, Karen must take at least 12 credits. (e) Karen must take Introduction to Operations Research. (d) If Karen takes either Integer or Nonlinear Optimization, she must also take Linear Optimization. (e) If she takes Data Mining, she must take Probability and Statistics. (f) Karen must take at least two of the following courses: Linear Optimization, Data Mining, Modeling & Simulation. (a) Formulate an integer programming model that will determine which courses Karen should take while minimizing the number of hours spent on her courses each week. Make sure to define your variables and give brief but descriptive labels for your constraints. (b) Solve your model using MATLAB's intlinprog function. (If your model in part (a) is not an ILP you'll need to convert it to one.) What is the result? (c) Suppose instead Karen has at most 30 hours of study time to spend on her courses. Formulate a model that maximizes the number of courses Karen takes subject to this time restriction and the other stated constraints. (d) Try to solve your model in part (e) using MATLAB's intlinprog function. What is the result?