Find the maximum value of P = x+6y

Question

Subject to the following constraints:

2x+4y<10

x+9y<12

X>0

y>0

P= ?

Answer 1

The first step is to graph the constraints and get the boundary points for the feasible region. To do this, I solve the first 2 equations for y and use the graphing calculator.

y=(10-2x)/4

y=(12-x)/9

I find the boundary points of the feasible region are:

(0,0)

(3,1)

(0,4/3)

(5,0)

I plug these into the P equation (I don't need to do (0,0), this will not be a max

P=3+6(1) = 9

P=0+6(4/3) = 8

P=5+6(0) = 5

The max value is P = 9