Compute expansion profits and expected value

A theme park currently operates on 2,000 acres with annual entries of 1,000,000 and sells: 250,000 single-day tickets at $80, 100,000 five-day tickets at $300, and 10,000 annual passes at $1,000. Assume an annual-pass holder visits 25 days/year. Operating assumptions: variable operating cost is $22 per entry; fixed operating cost is $20,000,000 per year; the land-owner fee is a percentage of revenue. Prices remain constant under all scenarios. Tasks: (a) Compute current annual revenue, total variable cost, land-owner fee at 5% of revenue, and profit. (b) Expansion Option A: acquire an adjacent 1,000 acres under terms that increase the land-owner fee from 5% to 10%. Assume entries and ticket sales scale proportionally with acreage (to 3,000 acres total). Fixed operating cost remains $20,000,000; variable cost per entry is unchanged. Compute profit under Option A. (c) Expansion Option B (bid): you may bid for the same 1,000 acres such that, if you win (80% probability), the land-owner fee remains 5% at 3,000 acres; if you lose (20%), you stay at 2,000 acres with the current 5% fee. Compute the expected profit of bidding and compare to (a) and (b). Recommend the best option. (d) Sensitivity: (i) What land-owner fee rate under 3,000 acres makes Option A’s profit equal to the current (no-expansion) profit? (solve for the break-even fee rate). (ii) Holding the fee at 10%, what variable cost per entry at 3,000 acres would make Option A tie the current profit? Show formulas and numeric results.