SOLUTION: A health club currently charges its 2,000 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that

Question 980540: A health club currently charges its 2,000 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? Round to the nearest cent.
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
PRICE___________CLIENTS_______________REVENUE
44_________________2000
44+1_____________2000-7
44+2____________2000-2*7
44+3____________2000-3*7
.
.
44+x___________2000-7x_____________(44+x)(2000-7x)

Revenue is y=(44+x)(2000-7x) which represents a parabola, convex upward. Being found in factored form, the zeros are easy to find; and the vertex, a maximum, occurs in the exact middle of the roots (zeros).
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