Solution: 750

Since both the inequalities are less than equal to, we can conclude that the lines and their point of intersection are included in the solution set.

Also, since the point (a,b) lies on the solution set of the inequalities above.

We need to solve the above inequalities just like any other equations by the method of substitution.

Substituting x = y/5 (since we want the maximum value of b which represents the y-coordinate) from second equation in the first equation we have,

                        y <= -15 (y/5) + 3000

                        or 4y <= 3000

                        or y <= 750

Therefore, the maximum value of y-coordinate is 750 and since the point (a,b) lies on the solution set of the inequalities.

 Therefore, maximum possible value of b = 750.