Question

Find the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Use a graphing utility to verify your results.

Answer 1

Answer:

Point (50,166.67)

Step-by-step explanation:

Incomplete question.

The Revenue function R(x) is

$R(x)=\frac{1}{1500} (150x^2-x^3), \,\,0\leq x \leq 100$

First, we calculate the first derivative

$R'(x)=\frac{1}{1500} (300x-3x^2)$

The second derivative is

$R''(x)=\frac{1}{1500} (300-6x)$

The point of disminihing returns for the function happens when the second derivative is equal to zero. This is the point where the concavity of the function changes. This happens at x=50:

$(300-6x)=0\\\\6x=300\\\\x=300/6=50$

$R(50)=166.67$

At point (50,166.67) the function of revenue will be in its point of diminishing returns.