Hey there! Sign in to join this conversationNew here? Join for free

D1 - Linear Programming (help needed!) Watch

Announcements
    • Thread Starter
    Offline

    13
    ReputationRep:
    Hi guys, could anyone give me some advice on how to do this question please, specifically part A and B, using the 'vertex testing method'? Thank you
    Attached Images
     
    Offline

    2
    ReputationRep:
    What do you think
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by GeologyMaths)
    What do you think
    I don't know - hence I posted here to receive help.
    Offline

    2
    ReputationRep:
    Do you know how to do it using the objective line? If so, what do you notice about the points that method gives you
    Offline

    20
    ReputationRep:
    they mean put in the x and y values at each vertex into the formula. the vertices are the points on the edge of the feasible regions where lines cross.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by the bear)
    they mean put in the x and y values at each vertex into the formula. the vertices are the points on the edge of the feasible regions where lines cross.
    You've confused me - so would (0,90) be one of the points in the feasible region? How would I find the other two? (i think there's only two others, how would you find the far right point in the feasible reason on the line 6y=x, it looks about 180,30)
    (Original post by samb1234)
    Do you know how to do it using the objective line? If so, what do you notice about the points that method gives you

    Not really - I know you set the objective line equal to some value and plot it and find a point, not entirely sure how to do it though to be honest with you.
    Offline

    2
    ReputationRep:
    (Original post by iMacJack)
    You've confused me - so would (0,90) be one of the points in the feasible region? How would I find the other two? (i think there's only two others, how would you find the far right point in the feasible reason on the line 6y=x, it looks about 180,30)



    Not really - I know you set the objective line equal to some value and plot it and find a point, not entirely sure how to do it though to be honest with you.
    Basically the way the objective line method works is say you want to maximize 3x+2y. You start off by plotting the line with it equal to some constant, say 3x+2y =10 for example. You would then move your ruler parallel to this line, as essentially what this is doing is making 3x +2y= a bigger number as you move your ruler. The point that maximizes/minimizes the function will therefore either be the last point the line touches still in the feasible region or the first, depending on what you're trying to do. Hopefully this makes sense and you should be able to see what is special about these points.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by samb1234)
    Basically the way the objective line method works is say you want to maximize 3x+2y. You start off by plotting the line with it equal to some constant, say 3x+2y =10 for example. You would then move your ruler parallel to this line, as essentially what this is doing is making 3x +2y= a bigger number as you move your ruler. The point that maximizes/minimizes the function will therefore either be the last point the line touches still in the feasible region or the first, depending on what you're trying to do. Hopefully this makes sense and you should be able to see what is special about these points.
    Alright - so say for example in the instance you take that 3x+2y = 10, does this mean you'd essentially plot points at (10/3,0) and (0,5) and draw the line, using a ruler move it parallel to the line and see at which vertex in the feasible region it first crosses?
    Offline

    2
    ReputationRep:
    Yep, you normally only have to draw one case of the line and then you just move it parallel to that line. You should also notice that this is also a vertex of the feasible region, so another option is that you don't draw the line at all and simply evaluate the function at each of the vertices
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by samb1234)
    Yep, you normally only have to draw one case of the line and then you just move it parallel to that line. You should also notice that this is also a vertex of the feasible region, so another option is that you don't draw the line at all and simply evaluate the function at each of the vertices
    So, say I found the vertex at which maximises/minimises the function using the optimum line or whatever, would I then solve the two lines equal to eachother in order to find the intersection coordinates? Thank you by the way
    Offline

    2
    ReputationRep:
    (Original post by iMacJack)
    So, say I found the vertex at which maximises/minimises the function using the optimum line or whatever, would I then solve the two lines equal to eachother in order to find the intersection coordinates? Thank you by the way
    If you do vertex method, you must solve simultaneously to find ALL the vertices of the feasible region and test ALL of them, even if there are some that it blatantly isn't going to be. Objective line you just read off co-ordinates from the graph really if you can. The method is complicated a bit if you get asked for integer solutions
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by samb1234)
    If you do vertex method, you must solve simultaneously to find ALL the vertices of the feasible region and test ALL of them, even if there are some that it blatantly isn't going to be. Objective line you just read off co-ordinates from the graph really if you can. The method is complicated a bit if you get asked for integer solutions
    Ahh thank you! What if the point of intersection when using the objective line method looks like it wont be easy to read off, would solving the two intersecting lines be a viable method to use? Thank you by the way you've been incredibly helpful
    Offline

    2
    ReputationRep:
    (Original post by iMacJack)
    Ahh thank you! What if the point of intersection when using the objective line method looks like it wont be easy to read off, would solving the two intersecting lines be a viable method to use? Thank you by the way you've been incredibly helpful
    Yeah of course you can always just solve to find the vertex if you need to, it does the same thing. If it asked for an integer solution and the vertex that maximized was say (6.5, 12.5) you would need to evaluate 4 times either side (so 6,12, 6,13, 7,12 7,13) and also you would need to check that these are actually in the feasible region i.e. satisfy the constraints of the problem
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by samb1234)
    Yeah of course you can always just solve to find the vertex if you need to, it does the same thing. If it asked for an integer solution and the vertex that maximized was say (6.5, 12.5) you would need to evaluate 4 times either side (so 6,12, 6,13, 7,12 7,13) and also you would need to check that these are actually in the feasible region i.e. satisfy the constraints of the problem
    Oh god, well that sounds like a load of fun then

    Thank you for all of your help.
    Offline

    2
    ReputationRep:
    (Original post by iMacJack)
    Oh god, well that sounds like a load of fun then

    Thank you for all of your help.
    No worries, let me know if you need help with anything else - can probably help with most maths questions unless you take weird modules, physics or chemistry as well
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by samb1234)
    No worries, let me know if you need help with anything else - can probably help with most maths questions unless you take weird modules, physics or chemistry as well
    That sounds great, thanks! Do you have Skype or something easier to converse on if I run into trouble? Cheers mate
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Break up or unrequited love?
    Help with your A-levels

    All the essentials

    The adventure begins mug

    Student life: what to expect

    What it's really like going to uni

    Rosette

    Essay expert

    Learn to write like a pro with our ultimate essay guide.

    Uni match

    Uni match

    Our tool will help you find the perfect course for you

    Study planner

    Create a study plan

    Get your head around what you need to do and when with the study planner tool.

    Study planner

    Resources by subject

    Everything from mind maps to class notes.

    Hands typing

    Degrees without fees

    Discover more about degree-level apprenticeships.

    A student doing homework

    Study tips from A* students

    Students who got top grades in their A-levels share their secrets

    Study help links and info

    Can you help? Study help unanswered threadsRules and posting guidelines

    Sponsored content:

    HEAR

    HEAR

    Find out how a Higher Education Achievement Report can help you prove your achievements.

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.