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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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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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
In P ' (x) = -0.6x + 75 = 0, where did the other numbers go to?
Derivative of a constant is zero. So the 2000 goes away.

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Other answers:

Why does it make the 2000 go away?
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?
No this is for Algebra 2.
Oh. Well theres the solution using calculus.
o.O
Sorry

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