Question

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = −0.5p + 150 where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue?

Answer 1

The Better Baby Buggy Co. should set the price of its buggies at $150 each to achieve the maximum revenue, according to the provided demand equation.

Step-by-step explanation:

To find the price at which the Better Baby Buggy Co. should sell its buggies for the largest revenue, we need to analyze the demand equation, q = -0.5p + 150. Here, q represents the number of buggies sold and p is the price per buggy. Revenue is calculated as the product of the number of items sold (q) and the price per item (p), which gives us the revenue equation R = pq. Substituting the demand equation into the revenue equation gives us R = p(-0.5p + 150) or R = -0.5p2 + 150p. To find the maximum revenue, we need to find the vertex of this quadratic equation, which occurs at -b/2a, where a is the coefficient of p2 and b is the coefficient of p. This yields a price p of $150 for the maximum revenue.

Answer 2

Price=150

Step-by-step explanation:

Total revenue (TR) is given by
`Price * Quantity`. We can get the quantity from the demand equation. Then

`TR= (150-0.5p)* p=150p-0.5p^2`

where p is the price. To find the maximum revenue we take derivatives with respect to the price and equalize it to zero

`(d)/(dp)TR=150-p=0`

solving for p we have that p=150