A museum charges Rs 40 per ticket and attracts 500 visitors daily
MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 2 · Quadratic Equations - Part 2
Problem
A museum charges Rs 40 per ticket and attracts 500 visitors daily. For every rupee decrease in the ticket price, the museum expects 25 additional visitors.
Let the decrease in price be Rs x.
(i) Express the daily revenue R (in rupees) as a polynomial in x.
(ii) Factorise the polynomial obtained in part (i).
(iii) For which two values of x will the revenue be zero? Interpret each value briefly.
(iv) Using your answer to part (ii), determine the ticket price that gives the maximum possible daily revenue and calculate that maximum revenue.