SOLUTION: Xin owns a business with 100 employees. He is downsizing his workforce and has determined for every two employees he terminates he can increase the pay of the remaining employees b

Starting condition is 100 employees with the average salary of $50,000.


After terminating two employees n times, the number of remaining employees is 100-2n

and the average salary of remaining employees is  (50000+2000n)  dollars.


The current payroll is then

    P(n) = (100-2n)*(50000+2000n)

and the problem wants you find the maximum of this quadratic function over n.


Since our quadratic function is the product of two linear binomials, 
we easily can determine the roots (the x-intercepts).  


    They are  n= 100/2 = 50           (from 100-2n = 0)  

         and  n= -50000/2000 = -25    (from 50000+2000n = 0).


The maximum of the function P(n) is located exactly at half way between 50 and -25, which is n= 12.5


But since n is an integer number, we round n to EITHER closest integer.


So, the problem has two solutions with the same maximum payroll:

    (1)  n= 12  gives  (100-2*12) = 76 remaining employees with the average salary of 50000+12*2000 = 74000 dollars
           
                                  with payroll 76*74000 = 5624000  dolars;

and 

    (2)  n= 13  gives  (100-2*13) = 74 remaining employees with the average salary of 50000+13*2000 = 76000 dollars
           
                                  with payroll 74*76000 = 5624000  dolars.