Profit of Selecting All
Profit of contacting all with the offer is
Profit(All) = NTB - NC = N (TB - C)
Profit > 0 if TB > C or K = TB/C > 1
K = expected Benefit/Cost ratio of a random contact
For N, T, B, C above, K = 0.6
Profit(All) = -$2,000,000
Can we improve profit by selecting a subset ?