z=3x+5y
x+y >= 2
3x-2y<= 6
-x+4y<= 8
Draw the area satisfying the three constraints. It is a triangle (with its interior). At least in the case of two variables, it is a property of linear functions (3x+5y in this case) that their extrema over a finite polygon are found in one of the vertices of the polygon. Therefore, compute the value of the function in the three corners of the triangle and choose the largest and the smallest.