Math: Max/Min Word Problems

[etalns]

Errg, finding this really hard, and hoping to see if I can find any mathematicians here who'd be willing to spare me a few seconds =)

The daily profit, P dolalrs, of a cotton candy vendor at the fair is described by the function P = -60x^2+240x - 80, where x dollars is the serlling price of a bag of cotton candy.

A) What should the selling price of a bag of cotton candy be to maximizze daily profits?

B) What is the maximum daily profits?

 

[Heisenberg]

Take the derivative, set it equal to zero, solve for x.

 

[jlee]

Originally posted by: Qosis
Errg, finding this really hard, and hoping to see if I can find any mathematicians here who'd be willing to spare me a few seconds =)

The daily profit, P dolalrs, of a cotton candy vendor at the fair is described by the function P = -60x^2+240x - 80, where x dollars is the serlling price of a bag of cotton candy.

A) What should the selling price of a bag of cotton candy be to maximizze daily profits?

B) What is the maximum daily profits?

Maybe I'm missing something (make that probably missing something)..but what determines the maximum daily profit? Where is the time allotted, what is the production cost, how much can you sell (ie how many people are working, basically)..?

 

[Soccer55]

A) If you take the derivative of the profit function and set it equal to 0, you will get a first degree function which you can solve to find x. Then you have the selling price for the cotton candy that will maximize your profits.
B) Take the x that you got in part A and put it into the original profit function P. That will give you the maximum daily profit.

-Tom

 

[da loser]

$2, $160?

 

[blahblah99]

are you taking calculus? cause if you are, this question shouldn't be difficult at all...
you take the derivative of that function, solve for the zeros, and use that to plug back into P.

The answer I got is $2 and $160.