Price and Revenue
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 45 of 51.
A juice stall sells 120 - 10p cups a day when a cup costs p dollars. Revenue is the money taken: the price times the number sold. So R(p) = p(120 - 10p).
Raising the price is a trade. Each cup earns more, but fewer cups sell. Charge nothing and you earn nothing. Charge 12 dollars and you sell none. Those are the zeros of R, p = 0 and p = 12.
Multiplied out, R(p) = -10p^2 + 120p is a parabola opening down, so the best price is its vertex, halfway between the zeros: 6 dollars. Then R(6) = 6(60), which is 360 dollars a day.
Challenge
A shop sells 200 - 25p phone cases a week at a price of p dollars each, so its weekly revenue is R(p) = p(200 - 25p) dollars. Find the most revenue R it can take. On the blank board, first write the best price as a p = ... line, then the revenue as an R = ... line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
2Completing the Square
Perfect Square TrinomialsThe Missing NumberCompleting the SquareIrrational AnswersWhen a Is Not 1Recap: Completing the Square5Complex Arithmetic
Adding and SubtractingMultiplyingThe ConjugateDividingA Pure Imaginary BottomRecap: Complex Arithmetic8Lines Meet Parabolas
Two CrossingsJust TouchingNo MeetingA Circle and a LineRecap: Lines and Parabolas