Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function . Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns.

Question

Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function  . Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns. ​​

Quizplus · Accepted Answer

The point of diminishing returns occurs when the rate of production starts decreasing. This happens when the second derivative of the production function is negative.

Let's first find the first derivative of the production function:

f'(t) = 11ea984b_b22f_af80_9029_29c80e06e157_TB4005_11

Now, let's find the second derivative:

f''(t) = 11ea984b_b22f_aee5_9029_c44827a8e584_TB4005_11

We need to find the value of t where the second derivative is negative.

11ea984b_b22f_aee5_9029_c44827a8e584_TB4005_11  is negative for all values of t.

This means that the rate of production is maximized at all values of t, and there is no point of diminishing returns.

Therefore, the answer is (B) None of the above.

Suppose That the Total Number of Units Produced by a Worker