Question

Maximize and minimize p = x + 2y subject to

Answer 1

Answer:

  Minimum: (x, y, p) = (6, 0, 6)

  Maximum: (x, y, p) = (2, 8, 18)

Step-by-step explanation:

I find it easiest to solve problems like this graphically. In the attached graph, we have reversed all of the inequalities, so that the feasible region is white, rather than shaded 4 times. I find this makes it much easier to see. The dashed lines indicate that the boundary lines are part of the feasible region (not part of the space outside the feasible region).

Once the slope of the objective function is determined, it is easy to identify the vertices of the feasible region that will maximize or minimize it. P is minimized when its line is closest to the origin. It is maximized when it is farthest away from the origin.

We find ...

  p is minimized at (x, y) = (6, 0), where p = 6.

  p is maximized at (x, y) = (2, 8), where p = 18.