linear

Yeah your working for the last part is correct

but what about the profit line i drew?

Which one is the profit line? You should make it clear.

I labelled it and said profit line but my hand writing is small its on the LHS corner

Oh I see it. But you need to do a few more lines than that if you are using the profit line method to find the minimum/maximum!

Its technically correct though

I prefer the test pointing but in the exam if we are asked the ruler method ? how we do it would i get the marks if i did a profit line like that

You draw multiple profit lines that are parallel, and the maximum is the point that touches the furthest profit line from the origin (along the x axis)

but like in all mark schemes I see they draw one profit line like the mark scheme you saw for this paper? do you get my point like

Yeah what you do is draw one line, and you use your ruler to slide along the page, keeping your ruler and the line parallel.

I just draw a few profit lines to make the method clear

ok but does it matter which x and y value you use?

I mean would i get the full marks for a ruler method i did on the question

For drawing an initial profit line. You could have 0.7x + 0.2y = anything as long as its got the correct gradient.

And yeah you would get the marks.

hi
here

so was my profit line wrong , cause mark scheme showed one

No. You was right with an initial profit line,
but you had to translate it paralelly until
it will have common point with the feasible region
because the point of this R can be solutions (meeting the criteria).
For minimum, translate it up to the closest point of region
(there can be only one common point with the region) (B point)
For maximum, translate it up to the most far point
of region (A point)

so can i draw a profit line in the feasible region so like crosses the feasible region? does it matter where u have to put it

Yes. Initially.
Fe, 2x+7y = c
can cross or not the feasible region depending on value of c.
But your question is wich c will be the maximum or minimum
so that the line has a common point with the region.
As c increasing the line moves upward paralelly, and when
c is decreasing the line moves downward.
The extremum is there where the line just touches the region
(in a node and there is no other common point with the region)
For this (x,y) c will maximum or minimum
When the profit line touches the polygon along a side
then all point of that side are solutions (these are linear combinations
of te two endpoint of the side)

yes i used the test point will i lose marks if i did both test pointing and ruler