Linear Programming - Optimisation

[eloisegrace]

Hello,

I was wondering whether VCAA can specifically test you on the sliding line methods for optimisation. I much prefer the corner point principal and understand it better. Will all questions just ask for the optimal points?

Thanks!
Eloise

[mathsTeacher82]

Hi Eloise,

Yes they can test the sliding line method. This is a direct copy-paste from the VCAA Study Design:

•    use of the graphical method to solve simple linear programming problems with two decision variables, and the sliding-line method and the corner-point principle as alternative methods for identifying optimal solutions

There was a question on last year's Exam 1 on sliding line method. But you don't want to look at that one yet... save the 2019 exams to do under trial exam conditions in November!

PS. Good to finally see a school choosing the Graphs and Relations module this year!

[S_R_K]

The "sliding-line method" is the fact that if a (linear) objective function is optimised at two points on the same line segment that forms part of a boundary of a feasible region, then the objective function is optimised at every point on that line segment.

Some important consequences of this:

1. If an objective function is optimised at every point on a line segment that forms part of a boundary of a feasible region, then its  gradient is equal to the gradient of that line segment.

2. If the gradient of an objective function is not equal to the gradient of any line segment that forms the boundary of a feasible region, then the objective function is optimised at a "corner point" (if it is optimised at all).

So you don't literally need to take out your ruler and slide it along the page, you just need to apply these facts.

See 2016 Exam 1, question 5 for an example.