Business Mathematics #1

Explore the revenue function as revenue equals price times quantity. Derive revenue from price functions tied to a demand function, e.g., R = 2Q and R = 4Q − 0.5Q^2.

Compute average revenue and average costs by dividing total revenue and total cost by quantity. Examine how average fixed costs and average variable costs shape with production.

Explore the profit function as total revenue minus total costs, with a quadratic revenue and linear cost; expand brackets and analyze profit regions via the graph.

Identify break-even points at q=4 and q=20 and the maximum profit at q=12, value 128, using first and second derivatives on a downward-opening quadratic.