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 Upper P (x )equals x squared minus 120 x plus 8600. A. How many players should be produced to minimize the marginal​ cost?

Answer 1

Answer:

60 players should be produced to minimize the marginal cost

Step-by-step explanation:

Following the problem instructions, the marginal cost function is:

$P(x) = x^{2} -120x+8600$

Then, to find the x players at $P(x)\alpha$ would has its minimum value, we have to find the first derivative as follows:

$\frac{dP(x)}{dx} =2x-120$

And the minimum value is determined when:

$\frac{dP(x)}{dx} =0$

Then, we solve for x, and these would be the players produced to minimize the marginal cost:

$0=2x-120\\x=\frac{120}{2} =60$

That means at least 60 thousand players must be produced in order to minimize the marginal cost.