Case 2: Backorders attractive: pDo
Now the TC expression in (2) includes a negative
term. The interesting question, from the algebraic
point of view, is whether or not this term can be
made sufficiently negative to outweigh the last two
nonnegative terms. It turns out this is indeed
always true. Using (2) it is difficult to make further
progress directly, but we can return to (1) and
obtain a different expression for the TC. In order
to clarify the logic of the analysis, we point out
what is the ultimate goal of the algebraic
manipulations that follow. We attempt to rewrite
the TC, if possible, in the following form: