Question

. marginal Profit The publisher of a fiction book expects a total profit from a recently published book that expected to sell for many years since the release of the boot, P and t are Related bythe fcenction P(t)= 850 t^2/t ^2 +20​ Find the publisher's marginal profit on this bookat year 10 ond then year 11. a. P (t) b. t=10 c⋅t=11

Answer 1

Marginal profit for the publisher at years 10 and 11 is derived by calculating the derivative of the profit function, P(t), and substituting t=10 and t=11 into this marginal profit function.

Step-by-step explanation:

The student's question is about finding the marginal profit for a publisher at year 10 and year 11 using the provided profit function P(t) = 850t^2 / (t^2 + 20). Marginal profit can be understood as the profitability of each additional unit sold—calculated as marginal revenue minus marginal cost.

To find the marginal profit at a specific year, we differentiate the profit function P(t) with respect to time t to obtain the marginal profit function, then substitute the given years into that derivative function.

To solve the problem:

1. First, differentiate the given profit function P(t) with respect to t to find the marginal profit function.
2. Next, evaluate the derivative at t=10 to find the marginal profit at year 10.
3. Similarly, evaluate the derivative at t=11 to find the marginal profit at year 11.

This approach helps us determine if the publisher should expect increasing or decreasing profit margins at those specific time points.