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?

- anonymous

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- anonymous

by the simultaneous solution of both lines

- anonymous

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

- anonymous

1/2,0 i mean

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## More answers

- anonymous

both the points lie on x-axis

- anonymous

mean they are the intersection of lines with x-axis

- anonymous

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?

- anonymous

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

- anonymous

x=0

- anonymous

y=0

- amistre64

2x-y≥1 is this a typo?

- anonymous

\[2x-y \ge 1\]

- anonymous

thats what my teacher put

- anonymous

oh i have to write the equtions instead of inequalities

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

5 in denominator?

- anonymous

this is how we get the corner points

- anonymous

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

- anonymous

that makes more sense thanks a lot

- anonymous

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

- anonymous

is it y=9-4x/5?

- anonymous

it was originally 4x+5y≤ 9

- anonymous

fine..what next?

- anonymous

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

- anonymous

then he has his answer as y ≤ 9-4x/5

- anonymous

oh ok

- anonymous

correct

- anonymous

what next?

- anonymous

the x should then be move to the other side

- anonymous

the 4x

- anonymous

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

- anonymous

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

- anonymous

thats correct

- anonymous

for that u r given two lines and first quadrant

- anonymous

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

- anonymous

maximum value liea at one of the corner points

- anonymous

lies*

- anonymous

ok that makes more sense

- anonymous

so r u fine with it now?

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