Question

Given p= -x^2 + 6x + 9 is the price per item when a quantity x is demanded, and given C(x)=9x+10. Using correct calculus notation and showing all work, find each of the following:

a) How do you compute the revenue function?

b) Compute the revenue function.

c) Compute the Marginal Revenue function.

d) How do you compute the Profit function?

e) Compute the profit function.

f) Compute the Marginal profit function.

g) Compute the value of x for maximum profit.

h) What is the maximum profit? [Ignore the value x=0].

i) Compute the price for the quantity x found in part g.

j) Show for certain that the x-value found in part g represents a MAXIMUM profit.

Answer 1

We have both price and cost as a function of quantity demanded (x). Let us represent them as equations.

a. Revenue is simply the income a company generates. Thus, the total revenue is Price x Quantity demanded = Px
b. Revenue = Price x Quantity Demanded

c. Marginal revenue is calculated by differentiating the revenue wrt quantity demanded (x)

(by differentiating the above function)
d. To compute the profit function, we simply subtract cost from price.
Price - Cost = Profit

Hope this helped!