# How do you calculate Up and Down Penalties on a Branch and Bound algorithm of a MILP?

My notes really don't explain this clearly at all, so I have no idea what to do.

If I have the following MILP:

In which I've been told to solve it using:

(a) Rule 1 (choose the variable with the largest max$\{p_D(x) ,p_U(U) \}$ ;

(b) Rule 3 (choose the variable with the smallest min$\{p_D(x) ,p_U(U) \}$

For:

$p_D(x) =$ down penalty ; $p_U(U) =$ up penalty

They arrive at the following calculation for up and down penalties, from the LP-relaxation:

Can someone please explain to me how they got to this calculation for penalties, because I haven't been told how to do it in my notes, thanks.