The detailed examples made this exceptionally interesting.
A minor nitpick: it is more accurate to draw the efficient frontier with axis-aligned line segments. To see why, consider points P=(1,1), Q=(3,2), R=(4,4). These points are all on the efficient frontier, because no point dominates any other in both cost and quality. But the straight line from P to R passes to the upper-left of Q, making it look as if Q is not on the efficient frontier. The solution is to draw the efficient frontier as (1,1)-(3,1)-(3,2)-(4,2)-(4,4). (It’s a bit uglier though!)
The detailed examples made this exceptionally interesting.
A minor nitpick: it is more accurate to draw the efficient frontier with axis-aligned line segments. To see why, consider points P=(1,1), Q=(3,2), R=(4,4). These points are all on the efficient frontier, because no point dominates any other in both cost and quality. But the straight line from P to R passes to the upper-left of Q, making it look as if Q is not on the efficient frontier. The solution is to draw the efficient frontier as (1,1)-(3,1)-(3,2)-(4,2)-(4,4). (It’s a bit uglier though!)
Good point, except in cases where can create any linear combination of any two solutions. But you can’t always do that.