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?

Question

anonymous · Answer

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 · Answer

the n value is unchanged by the 8000 so we can make the problem simpler by removing it

anonymous · Answer

any other questions tag me... please medal and fan if you can

anonymous · Answer

@cramos725  thanks so much for all the help, you really explained all the steps and that helps a lot

anonymous · Answer

no problem @icecream75