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anonymous
 one year ago
The tennis club charges each of its 80 members $100 per month. The owner estimates that for each decrease of $1 in the monthly fee, two new people will join. What monthly fee will generate the most income for the owners?
anonymous
 one year ago
The tennis club charges each of its 80 members $100 per month. The owner estimates that for each decrease of $1 in the monthly fee, two new people will join. What monthly fee will generate the most income for the owners?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so you need to develop a formula so both the price and number of members is dependent on the fee... the income is the number of members times the fee [i=mf] where i is income m is members and f is fee m is 80+2n where n is the number of dollars dropped f is 100n we substitute these two equations into the original i=mf and we get i=[80+2n][100n] we expand this into the equation i=800080n+200n2n^2 i=2n^2+120n+8000 the amount the price changes is dependent on the variables so we can isolate this from the equation: i=2n^2+120n the final income is greatest when 120n2n^2 is greatest. this is a negative quadratic so we can find the vertex and the n value for the point [x] will be our answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the n value is unchanged by the 8000 so we can make the problem simpler by removing it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0any other questions tag me... please medal and fan if you can

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@cramos725 thanks so much for all the help, you really explained all the steps and that helps a lot

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no problem @icecream75
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