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?

Question

contestada

Respuesta :

tisg1796 tisg1796 · Answer 1 · 2019-11-01T14:33:37+01:00

Answer:

60 players should be produced to minimize the marginal cost

Step-by-step explanation:

Following the problem instructions, the marginal cost function is:

[tex]P(x) = x^{2} -120x+8600[/tex]

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

[tex]\frac{dP(x)}{dx} =2x-120[/tex]

And the minimum value is determined when:

[tex]\frac{dP(x)}{dx} =0[/tex]

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

[tex]0=2x-120\\x=\frac{120}{2} =60[/tex]

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