Algebra

A club currently has
300
members who pay
$ 400
per month for membership dues. The​ club's board members want to increase monthly revenue by lowering the monthly dues in hopes of attracting new members. A market research study has shown that for each
$ 1 decrease in the monthly membership​ price, an additional
3 people will join the club. What price should the club charge to maximize​ revenue? What is the maximum​ revenue?

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  1. Suppose there are x price decreases.
    so, price is 400-x
    membership is 300+3x
    revenue is thus (400-x)(300+3x)
    = -3x^2+900x+120000

    So, just find the vertex of the parabola to determine price and max revenue.

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  2. Nsj

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