Hello Can someone help me with the following questions from Deterministic Optimization Question 1 (50 points) The admissions office at Tech wants to

Hello Can someone help me with the following questions from Deterministic Optimization

Question 1 (50 points)

The admissions office at Tech wants to determine how many in-state and how many out-of-state students to accept for next fall's entering freshman class. Tuition for an in-state student is $8,000 per year, whereas out-of-state tuition is $24,000 per year. A total of 12,000 in-state and 8,000 out-of-state freshmen have applied for next fall, and Tech does not want to accept more than 5,000 students. However, because Tech is a state institution, the state mandates that no more than 50-0.5% of the accepted students can be out-of-state students. From past experience the admissions office knows that 12% of in-state students and 24% of out-of-state students will drop out during their first year. Tech wants to maximize total tuition while limiting the total attrition to 720 first-year students

(Answers from QM or Excel solver are not accepted.)

a. (10 points) Formulate a linear programming model for this problem.

b. (10 points) Solve this model by using graphical analysis. Draw at least three iso-profit lines to determine the optimal solution. (QM graphs are not allowed)

c. (10 points) Give the coordinates of all extreme points. Calculate the total tuition at the extreme points and validate the solution you found in part b. (Show your work)

d. (20 points) Assume that the new president wants to maximize the number of accepted students while keeping the total tuition above $40 million. Formulate the problem and find the optimal solution (optimal number of accepted in-state and out-of-state students) via graphical approach (either use iso-profit lines or evaluate total accepted students at extreme points). (Hint: The feasible region is not the same as in parts a, b, and c.)

Question 2 (50 points)

Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 15 claims per day, whereas a temporary operator can process 10 per day, and on average the company processes at least 300 claims each day. The company has 36 computer workstations, and each operator needs one workstation. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.25 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $60 per day, and a temporary operator is paid $30 per day. The company wants to determine the number of permanent and temporary operators to hire in order to minimize costs.

(Answers from QM or Excel solver are not accepted for this question.)

a. (10) Formulate a linear programming model for this problem.

b. (10) Solve this model by using graphical analysis. Draw at least three iso-cost lines to determine the optimal solution. (QM graphs are not allowed)

c. (10) Give the coordinates of all extreme points. Calculate the cost at the extreme points and validate the solution you found in part b. (Show your work)

d. (20) Assume that the company has a daily budget of $1,200 for permanent and temporary operators' daily wages. The company wants to determine the number of permanent and temporary operators to hire in order to minimize defective claims per day. Formulate the problem and find the optimal solution via graphical approach (either use iso-cost lines or evaluate costs at extreme points).