Question

For the feasibility region shown below (will attach in a sec!!), find the maximum value of the function P=2x+3y.

*** there are no answer choices...

Answer 1

hi!!! i have like no idea how to do this :(

Answer 2

this is a linear programming problem

Answer 3

so first you need to identify the corner points

Answer 4

what are the corner points

Answer 5

(6,5)

Answer 6

that's one, what else

Answer 7

(0,8)

Answer 8

good, any others?

Answer 9

(8,0)

Answer 10

and finally...???

Answer 11

and (0,0)

Answer 12

the min and the max will result if you plug in one of those points into P = 2x+3y

Answer 13

so plug in each point into P = 2x+3y

Answer 14

will it be the same outcome?? or must i do all of them??

Answer 15

(6,5)
P=2(6)+3(5)
=12+15
=27

is that one right??

Answer 16

good, and the last one is?

Answer 17

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

Answer 18

plug in (0,0)

P = 2x+3y

P = 2(0)+3(0)

P = 0 + 0

P = 0

plug in (0,8)

P = 2x+3y

P = 2(0)+3(8)

P = 0 + 24

P = 24

Answer 19

what do i do now?? were those right? :D

Answer 20

So we have the following

(0,0) ---> P = 0
(0,8) ---> P = 24
(6,5) ---> P = 27
(8,0) ---> P = 16

which point yields the largest value of P?

Answer 21

largest point is 27???

Answer 22

so the max of P = 2x+3y is P = 27 given the restrictions in the graph

Answer 23

oops i meant (6,5) ??? haha is (6,5) the largest point??

Answer 24

that's the point that yields the maximum

Answer 25

the actual max is P = 27

Answer 26

so my answer is: P=27 ???

Answer 27

yes

Answer 28

okay!! thanks :D

Answer 29

np