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Revenue with Demand and Price in GeoGebra

You can use GeoGebra to find the revenue function and the demand.

  • If you want to find the revenue function R(x) when you have the price function p(x), go to Item 3.

  • If you want to find the demand that yields the greatest profit, and also use it to find the greatest revenue and the price of the product, go to Item 3.

  • If you want to find the demand when you have the revenue function R(x), go to Item 3.

GeoGebra Instruction 1

Find R(x) When You Have p(x)

1.
Open Algebra View under GeoGebra icon View in GeoGebra icon Menu.
2.
Enter the price function p(x) in an empty row in Algebra View, like this:

p(x) = <Expression>

where you replace <Expression> with your expression. Press Enter.

3.
In a new row in Algebra View, type

R(x) = Expand(x * p(x))

Press Enter. Your revenue function R(x) is displayed in the same row.

GeoGebra Instruction 2

Find the Demand that Yields the Greatest Profit

1.
Use Item 3 to get both the revenue function R(x) and the price function p(x) in GeoGebra.
2.
Find the greatest revenue by using the command

Extremum(<Polynomial>)

where you replace <Polynomial> with R. The x-coordinate of the point you get is the demand that yields the greatest revenue, while the y-coordinate is the greatest revenue itself.

Find the Greatest Revenue and the Price of a Product

3.
To find the price of the product, type

p(e)

where e is replaced by the value of the x-coordinate from the previous step. The value you get is the price that yields the greatest revenue. You can also type

(p, e(p))

which gives you a point on the graph of p(x) showing the price along with the point from the previous step.

Revenue function R(x), price function p(x), greatest revenue and demand in GeoGebra

GeoGebra Instruction 3

Find the Demand When You Have R(x)

If you have followed the instructions above, I recommend that you save the GeoGebra files from them now, close them, and open a new GeoGebra file.

1.
Open CAS under GeoGebra icon View in GeoGebra icon Menu.
2.
Type

R(x) := <Expression>

in CAS, where you replace <Expression> with your expression. Don’t forget the colon before the equal sign!

3.
In the next row, use the command

Solve(<Equation>, <Variable>)

where

  • <Equation> is replaced with p = R/x,

  • <Variable> is replaced with x.

GeoGebra will print an equation x = The right-hand side of this equation is the demand.

Demand d(p) that yields the greatest revenue in GeoGebra

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