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Mathhelp346
 2 years ago
AGLERA 2 HELP PLEASE:
The owner of a company that produces handcrafted music stands hires a consultant to help set the selling price for the product. The consultant analyzes the production costs and consumer demand for the stands and arrives at a function for the profit, P(x)=0.3x^2+75x2000, where x represents the selling price of the stands.
a.At what price should the stands be sold to earn the maximum profit?
Mathhelp346
 2 years ago
AGLERA 2 HELP PLEASE: The owner of a company that produces handcrafted music stands hires a consultant to help set the selling price for the product. The consultant analyzes the production costs and consumer demand for the stands and arrives at a function for the profit, P(x)=0.3x^2+75x2000, where x represents the selling price of the stands. a.At what price should the stands be sold to earn the maximum profit?

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Phydeaux
 2 years ago
Best ResponseYou've already chosen the best response.1P(x) = 0.3x^2 + 75x  2000 breakeven point is P(x) = 0 0 = 0.3x^2 + 75x  2000 use quadratic x = 30.35152757, 219.6484724 maximum profit is P ' (x) = 0 P ' (x) = 0.6x + 75 = 0 0.6x = 75 x = 75/0.6 = 125 P(125) = 0.3*125^2 + 75*125  2000 = 4687.5 + 9375  2000 = 2687.5 breakeven point < maximum; therefore breakeven is x = 30.35152757

Mathhelp346
 2 years ago
Best ResponseYou've already chosen the best response.0In P ' (x) = 0.6x + 75 = 0, where did the other numbers go to?

Phydeaux
 2 years ago
Best ResponseYou've already chosen the best response.1Derivative of a constant is zero. So the 2000 goes away.

Mathhelp346
 2 years ago
Best ResponseYou've already chosen the best response.0Why does it make the 2000 go away?

Phydeaux
 2 years ago
Best ResponseYou've already chosen the best response.1The derivative of a constant is 0. So you could write out +0, or realize thats a waste of time. Is this for a calculus class?

Mathhelp346
 2 years ago
Best ResponseYou've already chosen the best response.0No this is for Algebra 2.

Phydeaux
 2 years ago
Best ResponseYou've already chosen the best response.1Oh. Well theres the solution using calculus.
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