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).

(a) P(x)=(1-e⁻⁰˙⁰²⁵ˣ)(2000000)(3.25)-11250x=

6500000(1-e⁻⁰˙⁰²⁵ˣ)-11250x.

dP/dx=0.025(6500000)e⁻⁰˙⁰²⁵ˣ-11250=0 at maximum.

(d²P/dx²<0 indicating maximum.)

162500e⁻⁰˙⁰²⁵ˣ=11250,

-0.025x=ln(11250/162500)=-2.6703 approx.

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.