Optimize SaaS pricing and profit

A software company sells one seat per customer per month. Demand is q(p) = 10,000 − 50·p (units/month), variable cost c = $5 per seat, fixed monthly cost F = $100,000. 1) Derive the profit-maximizing price p* and quantity q* and compute the maximum monthly profit. Show your calculus. 2) If capacity is limited to 6,000 seats/month, what price maximizes profit under the constraint? 3) If a 10% price increase raises churn from 2% to 4% monthly (subscription setting), explain how your model changes and how you would estimate LTV-optimized price instead of static monthly profit.