Compute gala vs online break-even donors

A nonprofit has to select one of two possible fundraising approaches.

Option A (Gala): the event can hold 100 attendees; fixed cost is $20,000, and variable cost is $100 per attendee. There are two donor segments: High (H) donors give $1,000 each, and Low (L) donors give $250 each. In the broader donor pool, 80% are L and 20% are H. If k of the 100 gala attendees are H, then the remaining attendees are L.

Option B (Online campaign): it reaches 1,000 people; fixed cost is $8,000, and variable cost is $1 per person reached. Among those 1,000 reached, 80% are L and 20% are H. The conversion rates and average gifts are as follows: L donors convert at 8% and give $50 on average, while H donors convert at 15% and give $500 on average.

Questions:

1. Calculate the expected net revenue for Option B.
2. Write Option A's net revenue as a function of k. Determine the smallest integer k for which Option A's net revenue is at least Option B's expected net revenue.
3. If gala invitations are drawn at random from the pool (80% L / 20% H), calculate Option A's expected net revenue and its expected advantage over Option B.
4. How much would the gala's fixed cost need to increase, with all else held constant, to move the break-even k found in (2) upward by 10 additional H attendees?

Overview: This question assesses a candidate's ability to compute expected values, model revenue using probability-weighted segments, perform break-even analysis, and analyze the sensitivity of cost parameters in a donor-segmentation setting.