SOLUTION: A health club currently charges its 1,700 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that

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Question 907706: A health club currently charges its 1,700 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that each $1 increase in dues will result in the loss of 7 clients. How much should the club charge each month to optimize the revenue from monthly dues?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Monthly revenue goes this way:
(clients)*(membershipRate)
1700*44
(1700-7)*(44+1)
(1700-7-7)(44+1+1)
(1700-7x)(44+x)

Let x = dollar increase in membership monthly rate, and the monthly revenue is highlight_green%28%281700-7x%29%2844%2Bx%29%29 and the domain must be whole numbers. The function definition will be a parabola with a maximum. My solution response stops here unless you find more difficulty with this.