Question

maximize the objective function p = 3x+y sibject to the following constraints
4x+5y≤9
2x-y≥1
x≥0
y≥0
on my teachers answer sheet ht has 1/2,0 as his corner points
2.25,0 as another
1,1(which is the intersection of the two lines), how did my teacher get the other two corner points?

Answer 1

by the simultaneous solution of both lines

Answer 2

i saw the 1,1 with the intersection but did not find the (2.25,0) and the (1/2,)

Answer 3

1/2,0 i mean

Answer 4

both the points lie on x-axis

Answer 5

mean they are the intersection of lines with x-axis

Answer 6

i got the 1,1 intersection using my calculator but the 1/2,0 and 2.25, 0 did not come up. how would i find those?

Answer 7

\[4x+5y \le 9\]

Answer 8

x=0

Answer 9

y=0

Answer 10

2x-y≥1 is this a typo?

Answer 11

\[2x-y \ge 1\]

Answer 12

thats what my teacher put

Answer 13

oh i have to write the equtions instead of inequalities

Answer 14

the answers are y ≤ 9-4x/5 and y ≤ 2x-1

Answer 15

4x+5y=9
y=0 gives
x=9/4=2.25
point of intersection of the line and x-axis is (2.25,0)

Answer 16

likewise for the second eqn
2x-y=1
y=0
x=1/2
point is (1/2,0)

Answer 17

is the 5 in the deonominator a typo on his part?

Answer 18

5 in denominator?

Answer 19

this is how we get the corner points

Answer 20

on his answer key it says 9-4x/5

Answer 21

that makes more sense thanks a lot

Answer 22

so should i change the answer on the key where it says 9-4x/5?

Answer 23

is it y=9-4x/5?

Answer 24

it was originally 4x+5y≤ 9

Answer 25

fine..what next?

Answer 26

to draw the line transform it into eqn
4x+5y=9

Answer 27

then he has his answer as y ≤ 9-4x/5

Answer 28

oh ok

Answer 29

correct

Answer 30

what next?

Answer 31

the x should then be move to the other side

Answer 32

the 4x

Answer 33

which x?actually m not getting you what you actually want

Answer 34

u are to maximize the objective function subject to some constraints...right?

Answer 35

thats correct

Answer 36

for that u r given two lines and first quadrant

Answer 37

we draw the lines n mark the feasible region, just like explained in ur previous post

Answer 38

maximum value liea at one of the corner points

Answer 39

lies*

Answer 40

ok that makes more sense

Answer 41

so r u fine with it now?