anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
okay 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 100-n we substitute these two equations into the original i=mf and we get i=[80+2n][100-n] we expand this into the equation i=8000-80n+200n-2n^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 120n-2n^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
  • anonymous
the n value is unchanged by the 8000 so we can make the problem simpler by removing it
anonymous
  • anonymous
any other questions tag me... please medal and fan if you can

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anonymous
  • anonymous
@cramos725 thanks so much for all the help, you really explained all the steps and that helps a lot
anonymous
  • anonymous
no problem @icecream75

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