Revenue Function

All you need to find the revenue function is a strong knowledge of how to find the slope intercept form when a real life situation is given.

Then, you will need to use the formula for the revenue (R = x × p)

x is the number of items sold and p is the price of one item.

Real life example of the revenue function

After some research, a company found out that if the price of a product is 50 dollars, the demand is 6000. However, if the price is 70 dollars, the demand is 5000.

Find the revenue function. Then calculate f(4249), f(4250), and f(4251). What is your observation?

Revenue function

Solution or modeling the revenue function

Notice that the demand depends on the price of the product. The higher the price, the less the demand.

If x is the demand or how many items are sold and p is the price, we can then say that x depends on p.

As a point, you can write (p, x)

Notice that the dependent variable is always put on the right in the ordered pair.

There are two ordered pairs for the situation above. These are (50, 6000) and (70, 5000)

m =
x1 - x2 / p1 - p2

m =
6000 - 5000 / 50 - 70

m =
1000 / -20

m = -50

x = -50p + b

To find b, use (70, 5000)

Here p = 70 and x = 5000

5000 = -50 × 70 + b

5000 = -3500 + b

5000 + 3500 = -3500 + 3500 + b

8500 = b

x = -50p + 8500

x = -50p + 8500 is the demand equation and it depends on the price.

To find the revenue function, use R = x × p


To find p, use x = -50p + 8500 to solve for p

x = -50p + 8500

x - 8500 = -50p + 8500 - 8500

x - 8500 = -50p

Divide both sides by -50

x - 8500 / -50
 =   
-50p / -50

x - 8500 / -50
= p
x - 8500 / -50
 =   
-50p / -50

x - 8500 / -50
= p


R = x × p

R = x × (
x - 8500 / -50
)

R = x × (
x / -50
+ 170 )

R =
x2 / -50
+ 170x

Instead of using R, you can use f(x) to denote that it is a function

f(x) =
x2 / -50
+ 170x

f(4249) =
42492 / -50
+ 170 (4249)

f(4249) =
18054001 / -50
+ 722330

f(4249) = -361080.02 + 722330 = 361249.98


f(4250) =
42502 / -50
+ 170 (4250)

f(4250) =
18062500 / -50
+ 722500

f(4250) = -361250 + 722500 = 361250


f(4251) =
42512 / -50
+ 170 (4251)

f(4251) =
18071001 / -50
+ 722670

f(4251) = -361420.02 + 722670 = 361249.98

Notice that increasing the amount of items sold from 4250 to 4251 did not increase the revenue.

This means that the maximum money you can make with this revenue function is 361250 and you are better off selling 4250 items to maximize your revenue.

Recent Articles

  1. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes