Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.) S(t) = 7 â 6(cubedroot(t))

66.992%

Step-by-step explanation:

Since we want to maximize revenue for the government

Government's Revenue= Sales X Tax Rate

To maximize revenue, we differentiate R(t) and equate it to zero to solve for its critical points. Then we test that this critical point is a relative maximum for R(t) using the second derivative test.

Now:

Setting the derivative equal to zero

Next, we determine that t=0.6692 is a relative maximum for R(t) using the second derivative test.

R''(0.6692)=-3.48 (which is negative)

Therefore, t=0.66992 is a relative maximum for R(t).

The tax rate, t that maximizes revenue for the government is:

=0.66992 X 100

t=66.992% (correct to 3 decimal places)

i’m here for points.