Decision Maths

I'm currently doing question 1 of the mixed exercises for Edexcel Decision 1 for linear programming, but am confused on part e, where you ned to find the integer values to maximise profit. By using the ruler method, I know the for non-integer values, (4.8, 8) would b the point, but am unsure how this becomes (6,5) when using integers.

Mark scheme: https://www.activeteachonline.com/default/player/document/id/725743/external/0/uid/357726

(edited 6 months ago)

Reply 1

Muttley79

20

Original post by Amy.fallowfield

I'm currently doing question 1 of the mixed exercises for Edexcel Decision 1 for linear programming, but am confused on part e, where you ned to find the integer values to maximise profit. By using the ruler method, I know the for non-integer values, (4.8, 8) would b the point, but am unsure how this becomes (6,5) when using integers.

Mark scheme: https://www.activeteachonline.com/default/player/document/id/725743/external/0/uid/357726

I would try the points with integercoords nearer the bundary of the white area. Hard to see on the attached diagram.

Reply 2

Amy.fallowfield

OP

11

Original post by Muttley79

I would try the points with integercoords nearer the bundary of the white area. Hard to see on the attached diagram.

I tried that, but what confused me was that the intersection is in the middle of the top of one box, and the coordinate (6,5) is in the box below

Reply 3

Muttley79

20

Original post by Amy.fallowfield

I tried that, but what confused me was that the intersection is in the middle of the top of one box, and the coordinate (6,5) is in the box below

Did the coords give you a higher value though?

Reply 4

Amy.fallowfield

OP

11

Original post by Muttley79

Did the coords give you a higher value though?

(4.8, 8) gave me 28.8 and (6,5) gave me 28.5 so it is smaller, I'm just confused as to why we're looking that far away from the intersection because the textbook only looks at the points in the same box and (6, 5) is a different box

Reply 5

Muttley79

20

Original post by Amy.fallowfield

(4.8, 8) gave me 28.8 and (6,5) gave me 28.5 so it is smaller, I'm just confused as to why we're looking that far away from the intersection because the textbook only looks at the points in the same box and (6, 5) is a different box

You can only test coords with integer values - what do you mesn by 'box'? Test other points with integer coords if you aren't sure why.

Reply 6

mqb2766

21

Original post by Amy.fallowfield

(4.8, 8) gave me 28.8 and (6,5) gave me 28.5 so it is smaller, I'm just confused as to why we're looking that far away from the intersection because the textbook only looks at the points in the same box and (6, 5) is a different box

This (can) occur when the objective line/contour is almost parallel to the feasible space boundary (constraint lines). Here, the two bracketing integer points (4,9) and (5,7) both lie inside the freasible space (behind the constraint boundary) whereas the next two bracketing integer points (3,11) and (6,5) both lie on the constraint boundary. As those two points lie on the constraint boundary, you dont need to look x < 3 or x > 6 and those four points would be the only ones that need to be considered. If you sketched the objective line passing through (6,5), all the other three candidate integer solutions would lie to the left (have an objective value less than it) and no integer points would lie to the right (though (4.8,8) would be to the right).

Often for textbook questions, the objective line/contour and the constraints are less parallel and then the neighbouring values (x=4 and x=5 here) generally give the optimal integer point. Though in exteme cases where the objective line is arbitrarily close to being parallel to the constraint line,, the optimal integer solution can be far from the calculated non integer optimal solution

(edited 6 months ago)

Decision Maths

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