D1 - Linear Programming (help needed!)

What do you think

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.

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

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.

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

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

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.

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