SOLUTION: Maximize z = 2x1 + 3x2 subject to: 2x1 + x2 ≤ 10 9x1 + 3x2 ≤ 15 x1 ≥ 0, x2 ≥ 0

1)  In the quadrant QI, draw the feasible domain.


    In this problem, it is a triangle adjacent to x- and y-axes and bounded by the line 

        9x1 + 3x2 = 15.     (1)


    Find coordinates of its vertices.

    One vertex is (0,0), the origin of the coordinate system.

    Two other vertices are x- and y-intercepts of the line (2).


    


    Lines  2x1 + x2 = 10 (read) and  9x1 + 3x2 = 15 (green)



2)  Calculate values of the objective function at these three vertices.



3)  Of the three values of the objective function at vertices of the triangle choose maximum value.

    This value is the maximum value of the objective function in the feasible domain.

    The vertex which provides this maximum value, will give you the solution point to the problem.