By graphing the system of constraints, find the values of x and y that maximize the objective function.

Question

2x+y<=300
x+y<=200
x=>0
y=>0
maximum for p=x+2y

Answer 1

Graph the first two as lines
y= -2x+300 and
y=-x+300
then graph the positive x axis, and the positive y axis. Now the region within that four sided figure is the allowed region for x and y. However, we have a nice theorem which states that maximum and minimum of any objective funtion will occur on the boundry points. I can tell you the minimium will be at (0,0). The maximum with be at one of the other corners. You can see on the graph the four other corners, or you can solve for those points. Which one makes x+2y the greatest