(*Primal*)
Maximize[10x1+12x2,2x1+3x2≤16&&3x1+2x2≤19&&5x1+x2≤30&&x1≥0&&x2≥0,{x1,x2}]

(*Dual*)
Minimize[16y1+19y2+30y3,2y1+3y2+5y3≥10&&3y1+2y2+y3≥12&&y1≥0&&y2≥0&&y3≥0,{y1,y2,y3}]