Demand and revenue question: help?

[Jaimie]

A store has been selling 200 MP3 players a week at 300$ each. A market survey indicates that for each $10 rebate offered to the buyers, the number of sets sold will increase by 20/week.
a) find the demand function and the revenue function.
b) How large a rebate should the store offer to maximize its revenue?

a) Let n be the # of price increases
Let x be the number of MP3 players
Let p be the price of 1 MP3 player

x= 200 + 20n
x-200/20= 20n/20
1) n=x-200/20

2) d= 300-10n

sub 1 into 2
d(x)= 300-10(x-200/20)
d(x)= 400-x/2

r(x) = xd(x)
= 400 - x^2/2

b) after doing these steps...I am not sure what to do from here.
Can someone explain how to approach this step?

Thank you so much!

 

[mfb]

a) Let n be the # of price increases
Let x be the number of MP3 players
Let p be the price of 1 MP3 player

x= 200 + 20n

I think n is the number of price reductions, otherwise an increased price would increase the number of sold MP3 players.

x-200/20= 20n/20

Do you mean (x-200)/20=20n/20?
As x-200/20 = x-10.

d(x)= 400-x/2

r(x) = xd(x)
= 400 - x^2/2

The last line is wrong.

 

[Ray Vickson]

A store has been selling 200 MP3 players a week at 300$ each. A market survey indicates that for each $10 rebate offered to the buyers, the number of sets sold will increase by 20/week.
a) find the demand function and the revenue function.
b) How large a rebate should the store offer to maximize its revenue?

a) Let n be the # of price increases
Let x be the number of MP3 players
Let p be the price of 1 MP3 player

x= 200 + 20n
x-200/20= 20n/20
1) n=x-200/20

2) d= 300-10n

sub 1 into 2
d(x)= 300-10(x-200/20)
d(x)= 400-x/2

r(x) = xd(x)
= 400 - x^2/2

b) after doing these steps...I am not sure what to do from here.
Can someone explain how to approach this step?

Thank you so much!

I think you should start again, and be more careful and more explicit. For example, you could say something like:
S = number of MP3 players sold (per week) (was this your d?)
r = rebate (in $) (probably, your n)
p = selling price per player (in $)
Now give equations for S and p in terms of r. Then use those expressions to get revenue R ($ per week) in terms of the rebate, r. The result will be quite different from what you wrote.