Compute gala vs online break-even donors

Q: Compute gala vs online break-even donors

This question evaluates a candidate's skill in expected-value computation, probability-weighted revenue modeling, break-even analysis, and sensitivity analysis of cost parameters within a donor-segmentation context.

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Question

A nonprofit must choose one of two fundraising options. Option A (Gala): capacity 100 attendees; fixed cost $20,000; variable cost$ 100 per attendee. Donor segments: High (H) donate $1,000 each; Low (L) donate$ 250 each. Among the general donor pool, 80% are L and 20% are H. If k of the 100 gala attendees are H, the rest are L. Option B (Online campaign): reach 1,000 people; fixed cost $8,000; variable cost$ 1 per person reached. Of the 1,000 reached, 80% are L and 20% are H. Conversion rates and average gifts: L convert at 8% and donate $50 on average; H convert at 15% and donate$ 500 on average. Questions:

Compute the expected net revenue of Option B.
Express Option A's net revenue as a function of k. Find the minimum integer k such that Option A's net revenue is at least Option B's expected net revenue.
If gala invitations are random draws from the pool (80% L / 20% H), compute the expected net revenue of Option A and the expected advantage vs Option B.
By how much would the gala's fixed cost need to increase (holding all else constant) to raise the break-even k you found in (2) by 10 additional H attendees?

Compute gala vs online break-even donors

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