economic formula

[AmySaunders]

I've been given an economics problem in my calculus class. I have an example with a formula, from a previous assignment, but it doesn't seem to apply to my current problem.

Suppose that 1000 frankfurters can be sold every week at a food stand for $1 each. For every increase of $.20 per frankfurter, the number of frankfurters sold will decrease by 100. Write an equation which expresses the number of frankfurters sold as a function of price p in cents. What is the total revenue received from the sale of frankfurters per week if the price of each frankfurter is p?

I'm not sure how to even start on this equation. I do understand what the problem is asking.

Thank you for your help,

Anne Saunders

[stapel_eliz]

Suppose that 1000 frankfurters can be sold every week at a food stand for $1 each. For every increase of $.20 per frankfurter, the number of frankfurters sold will decrease by 100. Write an equation which expresses the number of frankfurters sold as a function of price p in cents. What is the total revenue received from the sale of frankfurters per week if the price of each frankfurter is p?

To learn how to set up this sort of exercise, please scroll down to the bottom of this page and review the "canoe rental" example.

[AmySaunders]

Thank you. I understand the canoe example, and that is actually how I began my problem, writing down concrete numbers and translating it to a formula, and figured that, for my problem, my equation was -20p^2+100p+1000. And they only ask for an equation, not an answer, so I figured I did not need to differentiate and set it equal to zero to get the maximum. I thought my equation would just be the answer. However, the back of the book says the answer is Q(p)=1500-5p and R(p)p =p(1500-5p).

[stapel_eliz]

...they only ask for an equation, not an answer....

Actually, the exercise appears to ask for a "sales volume" (or "demand"?) equation and then a revenue equation.

Write an equation which expresses the number of frankfurters sold as a function of price p in cents. What is the total revenue received from the sale of frankfurters per week if the price of each frankfurter is p?

[AmySaunders]

What do you mean by a sales volume equation? Or a revenue equation? I have never heard of either of them. Thanks for your help!

[stapel_eliz]

What do you mean by a sales volume equation? Or a revenue equation? I have never heard of either of them.

I mean this part:

Write an equation which expresses the number of frankfurters sold as a function of price p in cents. What is the total revenue received from the sale of frankfurters per week if the price of each frankfurter is p?

They ask for an equation for the number sold and then ask for the total revenue in terms of "p", which means another equation (or expression), rather than a numerical value.

If you've never dealt with equations before, then I'm afraid you need more help than can here be provided.