Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Why does it make the 2000 go away?

Answer 5

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?

Answer 6

No this is for Algebra 2.

Answer 7

Oh. Well theres the solution using calculus.

Answer 8

o.O

Answer 9

Sorry