#### boneybhaiya

##### New member

- Joined
- May 10, 2019

- Messages
- 1

I have a question for Linear Programming (Optimization). The basic idea is, an employer is giving salary to 6 employees, with minimum salary 500$ and maximum salary 5000$ subject to certain constraints like

x_i >= 500 (i = [1,2,3,4,5,6]

x_i <= 5000 (i = 1,2,3,4,5,6)

x_2 >= x_3

x_1 >= 300 + x_4

We need to minmize the total salary given out, which I've modeled with the above constraints and objective function

min x_1 + x_2 + x_3 + x_4 + x_5 + x_6

Theres a second part to the question which states what would the model be if we were to minimize the difference between the highest salary receiver and lowest salary receiver instead of the total salary given out

Essentially, something like

min (max (x_i) - min (x_i)) but using min and max "inside" is not allowed.

What is another way to represent that model?