The inequalities y≤−15x+3000 andy≤5x can be graphed in the xy-plane. They are represented by the half-planes below and include the boundary lines y=−15x+3000 and y=5x,respectively. The solution set of the system of inequalities will be the intersection of these half-planes, including the boundary lines, and the solution (a, b) with the greatest possible value of b will be the point of intersection of the boundary lines. The intersection of boundary lines of these inequalities can be found by setting them equal to each other: 5x=−15x+3000, which has solution x=150. Thus, the x-coordinate of the point of intersection is 150. Therefore, the y-coordinate of the point of intersection of the boundary lines is 5(150)=−15(150)+3000=750. This is the maximum possible value of b for a point (a,b) that is in the solution set of the system of inequalities.