D1 linear programming question

I am having problem on question 8(b), i have no clue how to start this question ... Can someone help me?

June 2014 QP - D1 Edexcel.pdf109.9KB

find the coordinates of all the corners, then find the values for k such that P is largest at D and lowest at A. (I have trouble putting this sort of stuff into words, I promise this makes sense in my head)

(edited 7 years ago)

Reply 2

alesha98

Original post by an_atheist

Why do i need to find all coordinates, not just the coordinates of A and D? And I know I need to use inequality, but I don't know how to set up the equations , can u explain furthermore?

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Reply 3

an_atheist

Original post by alesha98

You essentially have to do a comparison of P at the different points, for all values k. Once you have general formulae for the value of k at the corners you can find which corner has the highest and lowest values at the extremities (k=0 and k=a large number). See where you can go from there. (I'm trying to put what I'm doing into words, but its difficult)

Reply 4

alesha98

Original post by an_atheist

Sorry but I don't get it

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Reply 5

an_atheist

Original post by alesha98

Sorry but I don't get it

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You find the coordinates of all the points.
For each set of coordinates, you sub (x,y) values into the expression for P to construct a general formula
For a very small and a large value of k, find the values of the general formulae you found. This tells you which points you need to compare.
For the small value of k, compare the smallest value general formula and the general formula for A. Find where they become equal. k will be greater than this value.
For the big value of k, compare the largest general formula and that of D. Find where they intersect. k will be less than this value.
Thats how I did it at any rate

(edited 7 years ago)

Reply 6

alesha98

Original post by an_atheist

Where in the question tell me to find the coordinates of all vertex and compare them ?

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Reply 7

an_atheist

Original post by alesha98

Where in the question tell me to find the coordinates of all vertex and compare them ?

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It doesnt. he question says find the upper and lower limits of k such that when P=x+ky, the value of P at A is the minimum and at D the value is maximum.
Finding all the coordinates is a step in the process of finding those limits.

Reply 8

alesha98

Original post by an_atheist

Thanks, I will remember the process of finding the limits.

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Reply 9

tiny hobbit

Original post by alesha98

Thanks, I will remember the process of finding the limits.

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Or work with the gradient of the objective function, comparing it with the gradients of AB and DC. A sliding ruler must hit A first and D last.

Reply 10

an_atheist

Original post by tiny hobbit

Or work with the gradient of the objective function, comparing it with the gradients of AB and DC. A sliding ruler must hit A first and D last.

A valid method, but you need very steady hands. Doing it mathematically is longer but will never not work if you do it properly, and you'll get all those lovely A, B and M marks.

Reply 11

tiny hobbit

Original post by an_atheist

A valid method, but you need very steady hands. Doing it mathematically is longer but will never not work if you do it properly, and you'll get all those lovely A, B and M marks.

Do you know which question we are talking about? The gradient method here is an algebraic one, comparing the gradient of the objective line (which involves k) with the gradients of AB and DC.

In other questions, you may be told to use "the objective line (ruler) method", as was the case in June 2015. So don't write off this method, you may have to use it.