A computer training institute has 625 students that are payi

A computer training institute has 625 students that are paying $400 as the course fee. Their research shows that for every $20 reduction in the fee, they will attract another 50 students, which equation could be used to represent this situation, where x is the course fee and R(x) is the total revenue? R(x) = 2.5x^2 - 1625x R(x) = -2.5x^2 + 1625x R (x) = -3x^2 + 1650x R(x) = 3x^2 - 1650x A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. What fee should the school charge to maximize their revenue? $325

Solution

x is course fee

Lets assume y is no. of students: (x, y) = ( $400, 625)

$20 fee reduction leads to another 50 students ( $ 380 , 675)

find slope and then a linear equation : slope = ( 675 - 625)/(380-400) = 50/-20 = -2.5

y = -2.5x +c ; 625 = -2.5*400 + c ; c = 1625

y = -2.5x + 1625

So, R(x) = x*y = x(-2.5x + 1625) = -2.5x^2 + 1625x