Question

Maximize
P=8x+8y

Subject to
2x+y is less than or equal to 30
x+2y is less than or equal to 24
x, y is greater than or equal to 0

What is the maximum value of P?

Answer 1

i dunno, whats the average bladder hold these days... sorry :)

Answer 2

You only need to check the vertices of the polygon <(0, 0); (15, 0); (12, 6); (0, 12)>.

Answer 3

It's not enough to check the vertices, you also need to check how the function behaves between the vertices and inside the area decided by the constraints. Check for maximas and insert them into the function to see which point gives the highest value of P.

Answer 4

True, but this function is linear, thus it has no local extrema!

Answer 5

Ya, but for future assignments. :)