Simplex method in prime how to use the constrains maximise s.t. constraints.

[jte]

(11-03-2023 09:42 AM)Anthony The Koala Wrote:  ⋮
To jte,
I followed the procedure and here are the screenshots of the Advanced Graphics interface and the graph.



Furthermore I could not get the optimum solution of X = 2.85714, Y = 5.7143
* then the profit of X*6 + 5*Y = 45.713 as I did in my previous reply.
⋮

I could certainly have been more detailed in my earlier message... Plotting 5Y+6X=C in the Advanced Graphing app will plot a line for a particular value of C (to see the value, one could evaluate C in the home screen before going to the plot view).

The HP Prime doesn't currently have a built-in app for handling constrained optimization.

My plotting of SIN(1.5(6X+5Y))<0 was to show how 6X+5Y lay relative to the region of interest. If one plotted SIN(π*(6*X+5*Y))=0, for example, the plot would include 6*X+5*Y=K for each integer value of K; 6*X+5*Y would be increasing / decreasing perpendicularly to these contour lines.

Here is a plot with the contour lines:

   

From this sort of plot, I could visually see where 6*X+5*Y=K was first hitting the region of interest (as K increases from negative infinity). I could then toggle (check / uncheck) the various region constraints in the symbolic view to see which two where involved with the vertex of interest. I then added two equations that would define the boundaries (of each constraint). A screenshot of my symbolic view at this point is as follows:

   

And here is a plot view (I've adjusted the colours a bit, so that the lines are a bit easier to see, so that the region is not quite so heavy):

   

I added the two equations as the Advanced Graphing app does allow one to lock the plotting cursor to the intersection of two curves (via Trace / PoI / Intersections with...) — the two curves, in this case, being the two lines that together define the vertex of interest.