The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by
q = −3.5p + 1120
where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue?
p = $
What is the largest monthly revenue (in dollars)?
$

To find the price at which the company should sell the buggies to get the largest revenue, we first need to understand that the revenue $ R $ is given by the product of the price $ p $ and the quantity $ q $ sold:

\[
R(p) = p \times q
\]

We are given the demand equation for the buggies:

\[
q = -3.5p + 1120
\]

Substitute this into the revenue equation:

\[
R(p) = p \times (-3.5p + 1120) = -3.5p^2 + 1120p
\]

This is a quadratic equation in terms of $ p $, and the quadratic has the general form:

\[
R(p) = ap^2 + bp
\]

where $ a = -3.5 $ and $ b = 1120 $. The maximum value of a quadratic function occurs at the vertex, and the price $ p $ that maximizes revenue is given by the formula:

\[
p = -\frac{b}{2a}
\]

Substitute the values of $ a $ and $ b $:

\[
p = -\frac{1120}{2(-3.5)} = \frac{1120}{7} = 160
\]

So, the company should sell the buggies at **$160** per buggy to maximize revenue.

### Largest Monthly Revenue:
To find the maximum revenue, substitute $ p = 160 $ back into the revenue equation:

\[
R(160) = -3.5(160)^2 + 1120(160)
\]

Now let's compute this.

\[
R(160) = -3.5(25600) + 1120(160) = -89600 + 179200 = 89600
\]

Thus, the largest monthly revenue is **$89,600**.

### Summary:
- The optimal price is **$160**.
- The largest monthly revenue is **$89,600**.

Would you like further details on the solution? Here are some related questions you might find interesting:

1. How would the demand equation change if the price per buggy increased or decreased?
2. What if the company wanted to maximize profit rather than revenue?
3. How would you solve this problem graphically by plotting the revenue function?
4. What happens to revenue if the price is set lower or higher than $160?
5. How does the elasticity of demand affect pricing decisions?

**Tip:** Quadratic equations are helpful in optimization problems, especially in economics where maximizing profit or revenue is key.

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = −3.5p + 1120 where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue (in dollars)? $

Discover how to calculate the optimal price for maximizing revenue using the demand equation q = -3.5p + 1120 for Better Baby Buggy Co. Learn to apply quadratic functions and the vertex formula to solve this real-world business problem. Suitable for high school students in Grades 10-12.

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