Maximize x+y subject to x,y are both greater than or equal to zero. x+2y=16 ad 2x+y=20 and x+2y=16

Question

Finite math

Answer 1

graph the two lines

find their intersection point (8,4)

max x+y = 8+4 = 12

Answer 2

The way the question is asked, since there are only 2 equations (x + 2y = 16 and 2x + y = 20) they would intersect in one point.

 

Let x = 16 - 2y => 2x + y = 32 - 4y +y = 20

                        => 3y = 12 => y = 4 and then x = 8

 

With these values, both greater than zero, then x + y = 12, which has to be maximum since there is only point that satisfies all the conditions.