The director of the CO-Tech startup needs to decide what salaries to offer its employees for the coming year. In order to keep the employees satisfied, she needs to satisfy the following constraints: Tom wants at least $20 000 or he will quit; Peter, Nina, and Samir each want to be paid at least $5000 more than Tom; Gary wants his salary to be at least as high as the combined salary of Tom and Peter; Linda wants her salary to be $200 more than Gary; the combined salary of Nina and Samir should be at least twice the combined salary of Tom and Peter; Bob's salary is at least as high as that of Peter and at least as high as that of Samir; the combined salary of Bob and Peter should be at least $60 000; Linda should not make more money than the combined salary of Bob and Tom. (a) Write an LP that will determine salaries for the employees of CO-tech that satisfy each of these constraints while minimizing the total salary expenses. (b) Write an LP that will determine salaries for the employees of CO-tech that satisfy each of these constraints while minimizing the salary of the highest paid employee. (c) What is the relation between the solutions for (a) and (b)?