Number of donors=Rp where p is the population size (P=2000000). From this number of donors amount A=$Rpc is raised where c (c=$3.25) is the contribution per donor on average.
Net profit P=A-Cx where C is the costs per day (C=$11250/day).
dP/dx=0.025(6500000)e⁻⁰˙⁰²⁵ˣ-11250=0 at maximum.
(d²P/dx²<0 indicating maximum.)
Therefore, x=107 days approx. (P(107)=$4,848,355.62.) The campaign needs to run for 107 days for maximum profit.
(b) Maximum net proceeds are expected to come to about $4,848,356. R=0.9311 or 93.11% of the population.