Break-Even Analysis

Pre-Algebra · Axiom Academy

Every business has two lines — what it spends and what it earns. The break-even point is exactly where they cross. 1. Two Lines: Cost and Revenue Track two running totals as you sell cases. Total cost starts at the 200 you already spent and climbs 8 with every case. Total revenue starts at 0 but climbs faster — 20 a case. Plotted against the number of cases q , each total is a straight line. Total cost: a 200 head start, rising 8 per case Total revenue: starts at 0 , rising 20 per case 2. Break-Even Is Where They Cross Slide across the cases and watch the gap between the two lines. To the left, cost sits above revenue — that gap is your loss . The lines meet at the break-even point , where the gap is zero. To the right, revenue is on top and the gap is pure profit . The cost line is higher: C > R . You've sold some cases but haven't yet covered the 200 you spent. The two lines touch: C = R . Revenue exactly equals cost — no loss, no profit. The revenue line is higher: R > C . Every case past break-even adds 12 of profit. The vertical distance between the lines at any q is exactly profit = R - C . The lines cross between 16 and 17 cases, near the 333 mark. That's the break-even point we'll now pin down with algebra instead of eyeballing the graph. 3. Solving for the Break-Even Point

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