Welcome to Highline BI348 Class Video Number 59.
In this video we want to talk about what happens
if we can't get a solution.
Now this is the example we did in Video 57 and 58.
We've got an optimal solution using linear algebra
in Video 57, by finding the intersecting
lines in the vertice for our feasible region.
All the potential solutions that meet all the constraints
are in this region.
But out on the vertice, that was the optimal solution.
We also solved this problem using Excel.
And we solved and Excel told us at x equals 120-- that's
the number of laptops sold for Laptop number 1--
and at units of 100 for Laptop 2,
we're going to get our optimal solution of 10,400.
But sometimes Excel Solver will not give us an answer.
And so we need to look at three special cases and the error
message we will get from Excel Solver.
Let's go to our next slide, because we're going
to see Special Case Number 1.
It's called Infeasibility.
Now look at this chart right here.
And in particular, look at here's our equations.
And notice for each one of these we
have a comparative operator that's
pointing in a particular direction.
So the y value says, hey, if we're going to find a solution,
it's got to be all the y's up here.
The gray line says, hey, we've got to find something
this direction.
So that means potential solutions are up here.
But notice, we have one, two, three other lines, arrow,
arrow, arrow.
They're pointing in.
That means one, two separate regions with no overlap.
The message you'll get in Solver will say,
could not find a feasible solution.
Now what does this mean?
That means, given the set of constraints
and all of your inputs for your formulas,
you're not going to have a solution.
Perhaps you have to re-examine your constraints,
like this line, maybe you need to push it down.
Maybe it means that there actually is no solution,
because the constraints cannot be moved.
That's situation Number 1 in feasibility.
Let's look at the next slide.
Situation Number 2, Unbound.
Look at this chart.
We have these lines here.
And we can see that this one's pointing down.
This one's pointing up.
And this one's pointing to the side.
What does that mean?
It means our potential solutions go on forever.
The arrow just keeps pointing.
It's called unbound.
In general, it probably means you
have forgotten a constraint, so maybe you
need to add a constraint back in.
The message you'll get in Solver,
the object cell range does not converge.
Now Special Case Number 3, we have
to first talk about what's called
an optimal objective function contour line.
Now notice we got our solution, x equals 120, y equals 100,
and the amount was 10,400.
But if you set the original objective function exactly
equal to the optimal solution, that
means we can get many possible combinations of x and y
to give us our 10,400.
If we plot that line, that's called the function contour
line.
And that's going to be important to understand,
because when we look at our third situation--
and here it is-- we have a set of constraints
and we've plotted them.
But notice, here's our contour line.
And when I plot it, it's exactly on top
of one of the constraint lines.
That means, boom, I have many possible optimal solutions.
If I were to go from this point to this point,
many different x and y combinations
will give us our optimal solution.
Now a couple of videos ahead, we will
look at a situation like this and see
how to find a possible alternative solution.
If you go to slide 27, here are our steps
that we'll use a couple videos ahead,
to find our alternative optimal solution.
So this video we talked about alternative optimal solutions.
We talked about unbound.
And we talked about infeasibility.
Next video we're going to use Excel Solver to solve
a transportation shipping cost problem, where
our optimal solution will be our minimum cost.
We'll see you next video.