Express Maxima
How do I solve this supply and demand math question:Express the revenue R as a function of x. (x=-5p+100)?
Complete question:
The price p and the quantity of a product obey the demand equation x=-5p+100
Express the revenue R as a function of x.
What quantity x amximizes the revenue?
What is the maximum revenue?
this is a three part answer, please help???
I guess the revenue is the price times the number sold, x,
So
R = xp
To put this in terms of x only you have to solve the demand equation for p:
x=-5p+100
x-100 = -5p
p = 20 - x/5
Now put this into R above
R = xp = x(20 - x/5) = 20x - (x^2)/5
For part 2 you need to either graph this to find the max or you calculus methods to find the max.
For part 3 you just plug in that value of x into the R equation.
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