Find the values of x and y that maximize the objective function p=3x+2y for the graph. what is the maximum value?

Here, we are required to find the a combination of the values of x and y that maximize the objective function; P=3x+2y.

The values of x and y are 9 and 0 respectively, i.e at point (9,0).

The maximum value of P, at this point is;

P = 27.

First, it is important to know that the point of maximisation (i.e the combination of values of x and y where the objective function is maximized) is usually given by the coordinate of a vertex.

For point (0,8):

For point (5,4):

For point (9,0):

Therefore, the objective function is maximixed for values of x and y given by 9 and 0 respectively, i.e at point (9,0).

Therefore, the maximum value of P, at this point is;

P = 27.

Read more:

link

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

NOTE: I don't understand why (5,4) was given on your graph as a vertex.

(0,8): P = 3(0) + 2(8)  = 0 + 16   = 16

(5,4): P = 3(5) + 2(4)  = 15 + 8   = 23

(9,0): P = 3(9) + 2(0)  = 27 + 0   = 27      THIS IS THE LARGEST (MAX) P-VALUE

27