Calculate power and test duration

Assume baseline cold-food complaint rate is 3.50% and all such orders currently receive full refunds. The thermal-bag experiment targets a 10% relative reduction in complaint rate (to 3.15%). Using a two-sided z-test for two proportions with α=0.05 and power=0.80: (a) Compute the minimum sample size per arm for equal allocation; show formulas and numeric steps. (b) If only 60% of 200,000 daily orders are eligible and traffic is split 50/50, estimate the minimum test duration in days, assuming no seasonality. (c) Recompute (a) for a 6% relative reduction target. State all assumptions clearly and round final answers to the nearest 100 orders and 0.5 day.