Question

What point in the feasible region maximizes P for the objective function P = 2x + 3y?
Constraints: 2x+y≤15
x+3y≤20
x≥0,
y≥0

ive tried for so long but i have no idea..
answer choices:
A. (0,15)
B. (5,5)
C. (8,7)
D. (2,6)

Answer 1

are you able to graph the inequalities?

Answer 2

yes, I did that but i think i might of done it wrong..

Answer 3

can you draw it out?

Answer 4

this is what I got. I'm not sure if it's right becasue arent the intersection points supposed to be the answers?

Answer 5

that's a good rough sketch, so you have the right graph

where does each line intersect? In other words, what are the vertices of the boundaries?

Answer 6

the intersections are the testng points yes

Answer 7

the points from the intersections were not apart of the answer choices though , so i don't know what to do

Answer 8

now, if the options given are not a point of intersection, then you simply want to choose the one that is in the boundaries and makes P maximal

Answer 9

all of the answer choices are like 6.6666 for x or 5.76 or some not whole number and in the answer choices, all the numbers are whole

Answer 10

we can tell if a point is in the feasible region if it meets all of the constraints

Answer 11

for example: 0,15 is fine for eq1, but fails for eq2 ... its not in the region

Answer 12

so it doesn't have to be the exact intersecting point? it can just be in the intersection region?

Answer 13

its asking which option is in the feasible region, and maximizes P

Answer 14

first step, determine which options are in the feasible region, then test them out for maximum

Answer 15

Ohh okay, thank you!!

Answer 16

A and C do not meet the criterias, so we need to test the remaining points

Answer 17

I think it's b??

Answer 18

10+15 is bigger then 4+18 yeah

Answer 19

okay great, thanks so much

Answer 20

youre welcome

Answer 21

Here is the graph (I used Geogebra, which you can download for free)
Evaluate P at each "intersection point"
point (5,5) maximizes P= 2x+3y= 10+15= 25