6. The admissions office at State University wants to develop a planning model for next year's entering freshman class. The university has 4,500 available openings for freshmen. Tuition is $8,600 for an in-state student and $19,200 for an out-of-state student. The university wants to maximize the money it receives from tuition, but by state mandate it can admit no more than 47% out-of-state students. Also, each college in the university must have at least 30% in-state students in its freshman class. To be ranked in several national magazines, it wants the freshman class to have an average SAT score of 1150. Following are the average SAT scores for last year's freshman class for in-state and out-of-state students in each college in the university plus the maximum size of the freshman class for each college: a. Formulate and solve a linear programming model to determine the number of in-state and out-of-state students that should enter each college. b. If the solution in (a) does not achieve the maximum freshman class size, discuss how you might adjust the model to reach this class size. Problem 2 ( 35 points): Chapter 4 , Problem 36 (page 168 ) of our textbook. a. (10 points) In your PDF report, define your variables and formulate an algebraic model to maximize tuition dollars. Use good form (all variables on the LHS, etc.). b. (10 points) Create an Excel model to find the optimal solution, allowing fractional answers. Name this worksheet 2B. In your PDF report, present your solution clearly, as you would to a client. In your PDF report, comment on whether you would need to add integer constraints to this model. c. (5 points) Generate a Sensitivity Report and name its worksheet 2C. d. (5 points) Suppose that the original problem was revised to have an arts and science capacity of 1000 students. In your PDF report, show how the objective function would change according to shadow prices, without considering the allowable increases or decreases. Re-solve the model with the revised arts and science capacity, and name this worksheet 2D. In your PDF report, comment on whether the tuition dollars predicted by shadow prices matched what you obtained on worksheet 2D, and explain why or why not (using allowable ranges). e. (5 points) Suppose that the original problem was revised to have an engineering capacity of 1200 students. In your PDF report, show how the objective function would change according to shadow prices, without considering the allowable increases or decreases. Re-solve the model with the revised engineering capacity, and name this worksheet 2 E. In your PDF report, comment on whether the tuition dollars predicted by shadow prices matched what you obtained on worksheet 2E, and explain why or why not (using allowable ranges)