$20x2 per match is your baseline income per match here which I assume covers your costs.
1st try gets rejected, $20 bucks from the rejecter 2nd try gets rejected, $20 bucks from the rejecter 2rd try gets rejected, $20 bucks from the rejecter
So $60 a month should cover it, assuming that you have a 100% rejection rate.
$35 (.5 x 20 + .25 x 40 + .25 x 60) a month should cover it if you have a 50% rejection rate.
So assuming you have a 50% or less rejection rate, I would pay $35 a month for at-least a 7/8 chance of meeting someone every month.
$100/match to provide a guaranteed date would mean that your rejection rate is about 83%. Estimated using this forumula: (5 = x^1 + x^2 + ... x^n) and solving for x as the probability of rejection. I used an n of 29 for the estimate.
expected cost = cost of first match times probablity it is needed plus cost of second match times probability it is needed... plus cost of nth match times probability it is needed.
100 = 20x^0 + 20x + 20x^2...20x^n 5 = x^0 + x^1 ... x^n
The actual number is more like 72% :/