Question

The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand mp3 players is given by the function C(x) = x2−160x+8100.

A. How many players should be produced to minimize the marginal cost?

Answer 1

The optimal number of players to be produced to minimize the marginal cost is 80 thousand MP3 players.

Step-by-step explanation:

The marginal cost, denoted as C(x) = x2 - 160x + 8100, represents the cost of producing x thousand MP3 players.

To minimize the marginal cost, we need to find the minimum point on the marginal cost curve.

To do this, we can find the vertex of the quadratic function.

The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.

In the given function, a = 1, b = -160, and c = 8100.

Plugging these values into the formula, we get x = -(-160)/2(1) = 80.

Hence, the minimum marginal cost is achieved when x = 80, meaning that the optimal number of players to be produced to minimize the marginal cost is 80 thousand MP3 players.