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Answer:
The value is
Step-by-step explanation:
From the question we are told that
The amount charge per year is
The number of members it will have at this amount is
The amount amount increase that will lead to the loss of a single member is
Generally the total amount the club would obtain from its members is mathematically represented as
Now let x denote the number of member lost
Hence
=>
=>
Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero
=>
So from we have
So the amount the club should charge is