Thread: REVENUE questions

Denide is an artist who works at a shopping cneter drawing "pencil potraitts". SHe charges $20 per potraite and is averaging 30 potraits per week. she decides to increase the price , but every 1 doller increase she will lose one sale per week. it takes her $10 to make one potrait. wat should she set the price to get the max. profi.

Originally Posted by usm_67

Denide is an artist who works at a shopping cneter drawing "pencil potraitts". SHe charges $20 per potraite and is averaging 30 potraits per week. she decides to increase the price , but every 1 doller increase she will lose one sale per week. it takes her $10 to make one potrait. wat should she set the price to get the max. profi.

Let represent sales. Where represents the change in price. For example, if means that the price was increased by 1 dollar, then represents the sales. Since as you said she loses a sale for each dollar you have that because 30 without changing the price and 29 if increasing the price by 1 dollar.

We can create the first few values for and see how they affect the sales.

Do you see a formula? Yes,
.

Remember that,

In this case if she has to pay $20 for each sale since there are sales in total we have that,
.
Now, she recieves for every sale, because $20 was original and she increase the price by
But she makes sales thus in total she recieves thus,

Finally here profit is the difference between these values thus,

Open parantheses (use FOIL and watch those signs )

This is a parabola with a maximum point the max occurs at, in that case she has to increase her price by 15 dollars thus the new price would be 35 dollars.