what's the maximum value of y?

Question

y≤-12x+2400

y≤6x

 

In the xy-plane, if a point with coordinates (x,y) lies in the solution set of the system of inequalities above, what's the maximum value of y?

Answer 1

In the second inequality, multiply by -2 and add 2400 to get:

 

 -2y + 2400 ≥ -12x + 2400

 

This can be merged with the first inequality:

 

y ≤ -12x+2400 ≤ -2y + 2400

 

Now solve for y:

 

y ≤ -2y + 2400

 

3y ≤ 2400

 

y ≤ 800

 

So the maximum value of y is 800.