***** Corrected bersion based on the observation of your classmate - Raquel.
(The (2,2) entry of AA should be 2 instead of 3.)

******************************************************

Variables  x1 x2 x3 s_1- s_1+ s_2- s_2+ s_3- s_3+ s_4- s_4+

Minimize  Z = P1 (s_4-) + P2 (s1+) + P3 (s3+)  + P4(s2+)

Matlab commands:

A = []; b=[];

AA = [1.5 3 2 1 -1 0 0 0 0 0 0
3 2 2 0 0 1 -1 0 0 0 0
2 3 4 0 0 0 0 1 -1 0 0 
16 22 24 0 0 0 0 0 0 1 -1];

bb = [900 1550 1600 10500];

LB = [0 0 0 0 0 0 0 0 0 0 0];
UB = [];

g1 = [0 0 0 0 0 0 0 0 0 1 0];
[x,fval] = linprog(g1,A,b,AA,bb,LB,UB) 

g2 = [0 0 0 0 1 0 0 0 0 0 0];
AA = [AA;g1]; bb = [bb,0];
[x,fval] = linprog(g2,A,b,AA,bb,LB,UB) 

g3 = [0 0 0 0 0 0 0 0 1 0 0];
AA = [AA;g2]; bb = [bb,0];
[x,fval] = linprog(g3,A,b,AA,bb,LB,UB) 

g4 = [0 0 0 0 0 0 1 0 0 0 0];
AA = [AA;g3]; bb = [bb,50];
[x,fval] = linprog(g4,A,b,AA,bb,LB,UB)