A company’s profit, \( P \), is defined as revenue minus costs. If revenue is given by \( R = 50x \), costs are \( C = 30x + 100 \), and \( x \) is the number of units sold, express the profit function and find the profit when 20 units are sold.

["Building Profit Growth: Understanding a Company’s Revenue, Costs, and Profit", "In any business, profit is the ultimate indicator of financial success. Understanding how profit is calculated — revenue minus costs — is essential for managing operations and forecasting performance. This article explores the profit function for a company based on real-world pricing and cost structures.", "The Profit Formula", "Profit ( P ) is defined mathematically as:\n[\nP = R - C\n]\nwhere:\n- ( R ) = Revenue\n- ( C ) = Costs", "Given the expressions:\n- Revenue: ( R = 50x ) (where ( x ) is the number of units sold)\n- Costs: ( C = 30x + 100 )", "Substituting into the profit formula:\n[\nP = 50x - (30x + 100)\n]", "Simplifying the Profit Function\nDistribute the negative sign:\n[\nP = 50x - 30x - 100\n]\nCombine like terms:\n[\nP = 20x - 100\n]", "This linear profit function shows that for every unit of product sold, the company earns $20 in contribution margin, but incurs a fixed cost of $100 per period.", "Calculating Profit at 20 Units Sold\nTo find the profit when ( x = 20 ):\n[\nP = 20(20) - 100 = 400 - 100 = 300\n]", "Thus, selling 20 units yields a profit of $300.", "Understanding the profit function empowers business leaders to make data-driven decisions, control expenses, and optimize sales targets. For this company, every unit sold moves the profit forward—proving that strategic scaling translates directly into greater financial gain."]