BPP Q137 The cosmetic co

To draw the iso-contribution line, we use any level of contribution because whatever contribution we choose the lines will be parallel. We only need the angle of the line.

They have chose a total contribution of 6,400, simply because that is what the contribution will be if x was equal to zero.

However, again, by all means choose a different total contribution from 6,400. It will give a different line, but the line will be parallel.

This is all explained in my free lectures on linear programming. The lectures are a complete free course for Paper PM and cover everything needed to be able to pass the exam well.

(But do appreciate, as I explain in my lecture, that you can no longer we asked in the exam to actually draw the graph, but it will be tested that you understand the graph)

We need a line that fits nicely on the graph so that it can be rolled out to find the optimal mix of products.

If you look at the graph of the constraints, then if the line goes through the point x = 0 and y = 800 then it will be a sensible line.
At this point C = 8 x 800 = 6,400. We then carry on to find the other point using C = 6,400 and y = 0.

They could equally well have chosen the first point as being x = 0 and y = 1,000.
This would give C = 8,000, and continued in the same way.
Obviously the line would be different, but it would be parallel and that is all that is needed – the angle/gradient of the line.

Again, I explain this in my free lectures on linear programming.

You would be given full marks :0-)