Find the maximum value of P=x+6y

Step-by-step explanation:

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

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

goog may have it for you