Problem solving with quadratic functions.

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SUMMARY

The discussion centers on maximizing revenue for Eastern Ceramics based on the demand function p = 13 - 0.04q, where p is the price per flower pot and q is the quantity sold. Participants emphasize the need to express revenue R as a function of quantity sold, leading to the equation R = p * q. The optimal output level q that maximizes revenue is derived from the quadratic revenue function, which can be analyzed using techniques such as completing the square. The conversation highlights the importance of understanding the relationship between price, quantity, and revenue in quadratic functions.

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Familiarity with revenue calculation (R = p * q)
  • Knowledge of completing the square technique
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Learn how to derive revenue functions from demand equations
  • Study the method of completing the square for quadratic equations
  • Explore optimization techniques in calculus for maximizing functions
  • Practice solving real-world problems involving revenue maximization
USEFUL FOR

Students studying algebra, particularly those focusing on quadratic functions and revenue optimization, as well as educators looking for practical examples to illustrate these concepts.

davie08
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Homework Statement


Eastern Ceramics can sell up to 200 of its flower pots per day in accordance with the demand function.

p=13 -.04q

write revenue as a function of the quantity sold q. find the output level q that maximizes R and the selling price at this output level.

Homework Equations


The Attempt at a Solution



okay i tried to put my attempt on here but it was so far from the answer that it would likely confuse you lol.
 
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Then why post it here? At least, what did you use for the revenue function?
 
okay would you use R=a(q-h)^2 + k
 
davie08 said:
okay would you use R=a(q-h)^2 + k

Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV
 
Ray Vickson said:
Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV

I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.
 
davie08 said:
okay would you use R=a(q-h)^2 + k
What? Where did h, a, and q come from? Thats a general form for a quadratic but you need to use the information from this problem.

davie08 said:
I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.
If you sell 10 items for $5 each, how much money will you receive?

If you sell 50 items for $3 each, how much money will you receive?

How did you calculate that?

Okay, if you sell q items for p each, how much money will you receive?
 
davie08 said:
I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.

We do not do your schoolwork for you here on the PF. You are getting some very good hints, if you would just put forth some effort to try to understand and use the hints.
 
Posted from davie08:
okay would you use R=a(q-h)^2 + k

Ray Vickson said:
Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV

He is asking about a form appearing to completing the square as a way to solve, hoping the forum members recognize the standard form.

davie08, completing the square is one possible way to find the maximum, but first give us the complete description of the exercise, word-for-word. What is "p" supposed to be? What is "R" supposed to mean?
 

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