demand function is p(x)= 2x^2+10x+$1000 what is the R(x)

Answer 1

The demand function is the unit price (p(x)) at which x units of a product can be sold. In the case of the demand function:

p(x) = 2x² +10x + 1000

[Note: the coefficient of the x² term in a demand function is usually negative. Are you sure it's not -2x²?] If you produce 10 units of the product (x=10), you can sell each one for p(10)= 2·10² + 10·10 + 1000 = $1300 each. If you sell all 10 units, your revenue is $1300·10 = $13,000. Revenue, then, is the unit price p(x) times the number of units sold, x.

R(x) = p(x)·x = 2x³ + 10x² + 1000x