How to minimize the difference between maximum and minimum value in this LP? (Optimization)


New member
May 10, 2019
Hey guys,

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?


Elite Member
Dec 30, 2014
So are you having trouble with the first part? Can you show us your work so we can see where you are making any mistakes?