param w1; 
param w2; 

param PENALTY := 5;

var x1 <= 2, >= 2;
var x2 <= 2, >= 2;

var y1 >= 0;
var y2 >= 0;

minimize ObjPlusRecourse:
	 x1 + x2 + PENALTY * (y1 + y2);

subject to c1:
	w1 * x1 + x2 + y1 >= 7;

subject to c2:
	w2 * x1 + x2 + y2 >= 4;