Answer to Question #127959 in Calculus for Sheraz

Question

The demand function for a firm’s product is
q=150,000-75p
Where q equals the numbers of units demanded and p equals the price in dollars.
Determine the price which should be charged to maximize total revenue.
What is maximum value for total revenue
How many units are expected to be demanded?

Answer 1

1) Determine the price which should be charged to maximize total revenue.

Revenue = Price x Quantity.

Therefore. R= p(150000-75p)

R=150000p-75p²

The Derivative of Revenue function will be zero at its maximum.

R'=150000-150p*=0

150000=150p*

p*=$1,000.

(where p* is the price that will maximize total revenue)

2)What is maximum value for total revenue.

maximized total revenue (R*) is

R*= 150000(1000)-75(1000)²,

R*=$75,000,000

(Where R* is the value for total revenue)

3)How many units are expected to be demanded?

let units expected to be demanded be q*

q*=150000-75(1000)

q*=75,000