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?
Accepted Solution
A:
Answer:60 players should be produced to minimize the marginal costStep-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.