A firm's demand is p = 600 − 2q and its cost is C = 100q + 20,000. Without calculus: (a) find the revenue and profit functions; (b) find the output and price that maximise profit, and the maximum profit; (c) find the break-even outputs; (d) sketch the profit curve.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Revenue. R = (600 − 2q)q = 600q − 2q².
2 · Profit. P = R − C = −2q² + 500q − 20,000.
3 · Vertex. q = −500 ÷ (2 × −2) = 125; price = 600 − 250 = Rs. 350.
4 · Maximum profit. P(125) = −31,250 + 62,500 − 20,000 = Rs. 11,250.
5 · Break-even. q² − 250q + 10,000 = 0; D = 22,500; q = (250 ± 150) ÷ 2 = 50 or 200.
6 · Sketch. [Downward parabola: cuts q-axis at 50 and 200, peak (125, 11,250), y-intercept −20,000]
7 · Business link. Charging Rs. 350 rather than the revenue-maximising Rs. 300 earns more profit.