We've figured out that the Bulls can't keep Deng and get two MAX salary guys, even if they trade away for nothing, Gibson and Johnson. Since max guys are entitled to 30% of the salary cap, and the Bulls would want two, that would mean the remaining salary and cap holds can only add up to 40% of the salary cap, right?

Rose + Deng + Noah + 7 cap holds* = $23,334,924
$5,546,160 + $11,345,000 + $3,128,536 + ($473,604 × 7)
*the two players they would sign would eliminate two holds

Therefore, the salary cap needs to be $23,334,924 / 40%: $58,337,310

And we know that’s very, very unlikely (seriously, dammit).

If the projected salary cap of $56.1 million is true and the Bulls dumped Johnson and Gibson, then the Bulls would have: $32,765,076 in cap space. With a max salary of $16,830,000, that would leave :$15,935,076 in cap space. David Lee’s max, for example, would be $14,085,000.

They could keep Gibson, get James or Wade and Bosh and keep Deng.

If, however, they get rid of Deng for “nothing” (but let’s say they keep Gibson), they would have:$13,107,604 in committed salary. With two max guys, that would give them: $46,767,604, or $9,332,396 in remaining cap space. Who is available at shooting guard for that amount?

Which would you rather have?

A         B         C        D          E
Rose      Rose      Rose     Rose       Rose
James     Wade      Wade     $9 mil     Wade
Deng      Deng      James    James      ????
Lee       Lee       Gibson   Bosh*      Bosh
Noah      Noah      Noah     Noah       Noah + $9, cap space (Asik, shooters, etc. c’mon down!!!
                             *plus Gibson

With this information, what other scenarios are viable?

I think I'd take "D".