Why has the objective function changed from $M=x+y$ to $-M = -16 + 4x + 4y - S_3 - S_4$? I am studying optimisation and have come across an example of a maximisation problem:
maximise $$M=x+y$$
subject to $$x+3y \leq 32 \\ 2x+y \leq 24 \\x+3y \geq 6 \\ 3x+y \geq 10 \\ x,y \geq 0 $$
Apparently we can transform this into a minimisation problem:
minimise $$-M = -16 + 4x + 4y - S_3 - S_4$$
subject to $$x+3y + S_1 = 32 \\ 2x+y+S_2 = 24 \\ x+3y-S_3 + P_1 = 6 \\ 3x+y-S_4+P_2 = 10$$
I understand that the slack variables $S_1, S_2, S_3$ and $S_4$ have been introduced in order to make the constrains equal constraints. I understand that the pseudo variables $P_1$ and $P_2$ have been introduced to ensure that the tableau produced is feasible.
I am confused about the new objective function. i.e why has $M=x+y$ become $-M = -16 + 4x + 4y - S_3 - S_4$?

This is the Phase 1 of the Two-Phase Simplex method. You minimize the negative sum of $P_1$ and $P_2$ (artifical variables, pseudo variables).
$$x+3y-S_3 + P_1 = 6\Rightarrow -P_1=x+3y-S_3 -6$$
$$3x+y-S_4+P_2 = 10\Rightarrow -P_2=3x+y-S_4-10$$
The sum is $-M=-P_1-P_2=4x+4y-S_3-S_4-16$
An example with more detailed explanation can be seen here.
