Question

$y\le -15x+3000$
$y\le 5x$
In the xy plane, if a point with coordinates (a,b) lies in the solution set of the system of inequalities above, the maximum possible value of b is___

Answer 1

From the graph, it can be observed that the solution region for the inequality lies beneath each line. Hence, the maximum value of the y co-ordinate of the solution occurs at the point of intersection of the two lines.
To find the point of intersection, solve the equations of the lines y= -15x+3000 and y=5x
Equating the right sides of both equations directly, we get
5x= -15x+3000
$\Rightarrow 20x=3000$
$\Rightarrow x=150$
So, y=5x=750
Hence, the maximum possible value of b is 750.