Simultaneous Kelly where sum of all stakes must equal 100% BR

[VLR100]

Say a gambler has four uncorrelated simultaneous bets with positive expectations (say Kelly stakes of 2%, 3%, 4% and 5%). If the gambler had to bet his entire bankroll on this series of four simultaneous events (of course they're sub-optimal stakes), would the optimal stakes be (roughly?) equal to the kelly stake divided by the sum of all stakes for each bet? E.g. for the first bet: .02/.14 = 14.2857%.

Alternatively, if anyone can point me to some equations where a simultaneous kelly utility function is maximized subject to the constraint that the sum of all stakes = 100%, I would be very grateful.

Edit: Apologies for this silly question. Simply let the kelly multiplier tend to infinity and you've got a solution.

[chunk]

Over 12 hours and no response. Personally, I don't think that it's not that someone wouldn't understand the math, it's more likely that they would understand that it's much ado about nothing.

[Thremp]

chunk,

He posted the solution.