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The total revenue $ R $ earned per day (in dollars) from a pet-sitting service is given by $ R(p) = - 12 p^2 + 150p $, where $ p $ is the price charged per pet (in dollars).

(a) Find the revenues when the price per pet is $ \$4 $, $ \$6 $, and $ \$8 $ .(b) Find the price that will yield a maximum revenue. What is the maximum revenue? Explain your results.

a) $408,468,432$b) $x_{\max }=\$ 6.25$$R_{\max }=\$ 468.75$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Eleni K.

April 4, 2022

Determine if the following algebraic expressions are True or False.

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total revenue earn per day is given by the following expression if P is the price that you're charging per pet. So for part A, we'd like to know the revenue that we get when the prices, either for six or a saw, we simply do is just replace P with four, six or eight in the formula for our And if you simplify that, you should get one hundred eight four hundred eight and let's go ahead and include the unit there. This is in dollars if you plug in six, this is what your expression should look like, and that comes out to be four hundred and sixty eight. It's a comma there and then finally plug in eight. In this time, we actually make less money than the previous will make for thirty two. So now if let's goto Part B. And first, let's realize that if you would autograph this thing out, which we don't have to do a detail here, it is a problem that opens downward. This means that the max value will be the Vertex, and if you have a quadratic such as the one that we have, then the Vertex is always given by the point. So we see and all we need is A and B These air the coefficients in front of X squared and X In our problem, we see a is minus twelve and we see b is one fifty. So we'd like to find the price. This is a P value that gives them max revenue. So in other words, we're trying to find the X coordinates of the Vertex. That's the P value that gives you the largest y value. So that's negative. B. So that's negative. One fifty over two times negative twelve. You could cancel the negatives and simplify this. Or let's just go ahead and write to sense the decimal, since we're dealing with dollars, so it's six dollars and twenty five cents. So this price gives Max revenue, and now we'LL also find out what that revenue is. So that's the first answer for Part B, and then the last. The answer is that match revenue. This is equal to the revenue that you obtain when you plug in the P value that we just found. So plugging this into the formula for our gives you four hundred sixty eight dollars and seventy five cents

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