This chart has the same exact axes as we used before.
The horizontal axis plots demand from 6,000 all the way up to about 12,000.
The vertical axis is plotting sales.
And sales, we'd like it to be s i is equal to the minimum of d i and q.
The constraints are only going to insure that s i is less than or
equal to the minimum of d i or q.
So let's plot the two constraints.
The first constraint is s i is less than or equal to d i.
And the boundary of that constraint Is a line of slope one,
you can see when DI 6,000 in the lower left then,
SI less than equal to DI is going to limit SI to be below the line of at 6,000.
Same thing at 8,000.
If di were 8000.
Then si is less than or equal to di, is going to limit si to be 8,000.
If di were to be above 8,000, si.
So, for example, 9,000.
Si less than or equal to di, would force si to be less than or equal to 9000.
For each Si, there is a second constraint, Si is left center equal to Q.
And I'm plotting it here for Q = 8,000.
Again, in this case, no matter what Di is,
Si left center equal to Q is going to limit Si to be less center equal to 8,000.
Now we can see how as di changes,
as the demand for the ith sample differs,
a different constraint is going to end up being binding in the optimal solution.
So for example, if di were 7,000, if that sample were 7,000, Si would live there.
And in maximizing Si, Si less than or equal to Di would be binding.
So Si will be push up to 7,000 and then stop in the optimal solution.
If on the other hand, di were 9,000, if demand for
that sample were 9,000, si will leave over here and
in maximizing si in the optimal solution.
The binding constraint would be si less than or equal to q.