Why the maximum is always at a vertex

Once you have the feasible region, you do not have to test every point in it. Evaluate revenue $3c + 2d$ at each vertex: the origin where nothing is made, the flour-limited intercept on the cookie axis, and the flour-limited intercept on the donut axis.

Now think about the edges. Along an edge, revenue climbs steadily from the lower corner to the higher corner, so any point in the middle of an edge earns something in between, never more than the better corner.

Finally consider a point sitting in the interior of the region. From there you can always nudge toward more cookie mix or more donut mix and earn more, so an interior point can never be the best. Putting these together: the maximum revenue always sits at a vertex, so the search only needs to compare vertices. Plug each corner's coordinates into $3c + 2d$ to see which one wins in this two-mix case.