Question

The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by

q = −3p + 258,

where q is the number of buggies the company 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 the Turbo at $43 per buggy to achieve the largest revenue, based on the given demand equation and by finding the maximum of the revenue function.

Step-by-step explanation:

To maximize the revenue from the sale of the new Turbo model buggy, we need to find the price that yields the highest revenue, given the demand equation q = -3p + 258. Revenue (R) is calculated by multiplying the price (p) per buggy by the quantity sold (q), so we have R = p × q. Substituting the demand equation into the formula for revenue, we get R = p × (-3p + 258).

To find the maximum revenue, we first expand the revenue equation to R = -3p^2 + 258p and then take the derivative with respect to price to find the critical points, giving us R' = -6p + 258. Setting the derivative equal to zero to solve for p, we get p = 43.

Therefore, for the largest revenue, Better Baby Buggy Co. should set the price of the Turbo at $43 per buggy.