Question

The following function shows the relationship between the selling price (s), and profit P(s), in dollars, for a company.

P(s) = -20s2 + 1,400s - 12,000

Which statement best describes the intervals where the company's profit increases, decreases, or records a maximum?

It is least when the selling price is $35.

It is greatest when the selling price is $35.

It decreases when the selling price increases from $10 to $35.

It increases when the selling price increases from $35 to $100

Answer 1

@jdoe0001 @dugalde

Answer 2

It decreases when the selling price increases beyond $35.

Answer 3

hmm how did you get 35 anyway?

Answer 4

Please explain @dugalde

Answer 5

anyhow... do you know how to get the vertex of a parabolic equation, or quadratic?

Answer 6

p(s)=-20(s^2-70s+60)

Answer 7

Yes

Answer 8

the vertex is 35, 12500

Answer 9

@jdoe0001 Do you think the right answer is C

Answer 10

@jdoe0001 are you there?

Answer 11

the quadratic is has a negative leading term coefficient, -20
meaning the parabola opens downward or

so the maximum profit will occur at the vertex of the parabola
\(\bf p(s) = -20s^2 + 1,400s - 12,000\implies p(s)=20(-s^2+70s-600)
\\ \quad \\

\textit{vertex of a parabola}\\ \quad \\
p(s) = {\color{red}{ -1}}s^2{\color{blue}{ +70}}s{\color{green}{ -600}}\ \quad
\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)