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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+75x-2000, 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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1. Phydeaux

P(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

2. Mathhelp346

In P ' (x) = -0.6x + 75 = 0, where did the other numbers go to?

3. Phydeaux

Derivative of a constant is zero. So the 2000 goes away.

4. Mathhelp346

Why does it make the 2000 go away?

5. Phydeaux

The 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?

6. Mathhelp346

No this is for Algebra 2.

7. Phydeaux

Oh. Well theres the solution using calculus.

8. Mathhelp346

o.O

9. Phydeaux

Sorry

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