Final answer:
The Better Baby Buggy Co. should sell its buggies at a price of $190 each in order to achieve the largest monthly revenue. When buggies are sold at this price, the company can expect its largest monthly revenue to be $125,050.
Step-by-step explanation:
The problem at hand requires determining the price point for the Better Baby Buggy Co. to maximize its revenue given the demand equation q = -3.5p + 1330, where q is the number of buggies sold per month and p is the price per buggy. To find this price, we need to maximize the revenue equation. Revenue (R) is found by multiplying the price (p) by the quantity (q), so our revenue equation based on the demand equation is R = p × (-3.5p + 1330).
To find the maximum revenue, we need to find the vertex of the parabolic curve that this equation represents. This involves completing the square or using calculus to find the derivative and setting it to zero. Since the coefficient of p^2 is negative (-3.5), we know that the parabola opens downwards, and thus the vertex will give us the maximum point. The price at which revenue is maximized is found by setting the derivative of the revenue function to zero:
Revenue Function: R = p × (-3.5p + 1330) = -3.5p^2 + 1330p
Differentiate and set to zero: -7p + 1330 = 0
Solving for p: p = 1330/7 = 190
Therefore, the price p to obtain the largest revenue is $190 per buggy. The largest monthly revenue is found by substituting p back into the revenue function:
Largest Monthly Revenue: R = -3.5(190)^2 + 1330(190) = $125,050