Match club charges annual membership dues of 100 pesos per member, less 0.50 cantavo for each member over 600 and plus 0.50 centavo for each member less than 600. How many members should give the club most revenue from annual dues?

Answer 1

they get a credit of .5centavo for each member over 600, and a .5centavo for each memember less than 600. If that is true, they are getting zero net adjustments for all members from 0 to infinity.

revenue=100*members
max revenue is when members = infinity.

Answer 2

for x members (assuming you meant 50 centavos, not 0.50 centavos)

r(x) =
x(100+.5(600-x)) for x < 600
x(100-.5(x-600)) for x > 600

These are really the same function:

r(x) = 400x - 0.5x^2

maximum revenue is at x = 400