SOLUTION: A student club on a college campus charges annual membership dues of P800.00, less P5.00 for each member over 50. a.How many members would give the club the most revenue for a

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Question 1054898: A student club on a college campus charges annual membership dues of P800.00, less P5.00 for each member over 50.
a.How many members would give the club the most revenue for annual dues?
b.If the club considers only the number of students (bigger than 50) that will maximize the revenue, what is the amount of the maximum revenue that will be realized by the club?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A student club on a college campus charges annual membership dues of P800.00, less P5.00 for each member over 50.
a.How many members would give the club the most revenue for annual dues?
let x = no. of students over 50
total revenue = r(x)
r(x) = (50+x)(800-5x)
FOIL
r(x) = 40000 - 250x + 800x - 5x^2
A quadratic equation,
-5x^2 + 550x + 40000 = 0
max rev occurs on the axis of symmetry, x = -b/(2a) where a=-5; b=550
x = %28-550%29%2F%282%2A-5%29
x = +55
50 + 55 = 105 students would give max revenue
:
b.If the club considers only the number of students (bigger than 50) that will maximize the revenue, what is the amount of the maximum revenue that will be realized by the club?
Find the cost for each student if 55 more the 50 join
800-(55*5) = $535
Find the revenue if 105 students pay this amt
105 *525 = $55,125