# Linear problem, need a little help. :)

• Oct 18th 2008, 07:09 AM
entrepreneurforum.co.uk
Linear problem, need a little help. :)
Ok i have this homework set for my A level H.W and i need a little help on finding the objctive function.

question =

100x + 150y

4x + 4y </= 600
x + 6y </= 480
x,y >/= 0

Note: </= is less than or equal to for this example :)

I'm stuck on finding this part of the question

100x + 150y

i've put in a number which both goes into

100x + 150y = 300
which leaves me with x=3, y=2

and when i plot that onto a graph it doesn't fit well because all the other answers are much larger.

Any help would be great! :)

thanks
• Oct 19th 2008, 02:40 AM
CaptainBlack
Quote:

Originally Posted by entrepreneurforum.co.uk
Ok i have this homework set for my A level H.W and i need a little help on finding the objctive function.

question =

100x + 150y

4x + 4y </= 600
x + 6y </= 480
x,y >/= 0

Note: </= is less than or equal to for this example :)

I'm stuck on finding this part of the question

100x + 150y

i've put in a number which both goes into

100x + 150y = 300
which leaves me with x=3, y=2

and when i plot that onto a graph it doesn't fit well because all the other answers are much larger.

Any help would be great! :)

thanks

This is a linear program the constraints:

4x + 4y </= 600
x + 6y </= 480
x,y >/= 0

define a feasible region, and the objective to be maximised is

O(x,y)=100x + 150y

Now the for a linear program the objective achives its maximum at a vertex of the feasible region unless it is parallel to an edge when it achives its maximum all along the edge.

So here we find all the vertices of the feasible region and evaluate the objevtive at them and the one where the objective is largest is the optimal point (if two of them both give the maximum of the objective then all the points along the edge of the feasible region conecting those vertices are optima).

CB