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)?