1.  Simplify your constrain equations:

    5x + 15y >= 15   is equivalent to  x + 3y >= 3;

    5x +  5y >= 35   is equivalent to  x +  y >= 7.


2.  Your plot is this:





Plots y =  and y = 7-x


3.  Your domain is the INFINITE domain in the quadrant QI restricted by the x- and y- axes and by the red straight line.


4.  Find the intercept points for this line.


5.  According to the linear programming method, you need to evaluate the objective function in these two intercept points.

    Then choose one of the two pints, where the objective function is minimal.


6.  This point will be your solution.