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 C left parenthesis x right parenthesis equals x squared minus 120 x plus 7500.C(x) = x2−120x+7500.

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

B. What is the minimum marginal​ cost?

Answer 1

Solution:-

According to question

Marginal cost

For minimum marginal cost

2x-120 +0=0

2x= 120

x=120/2

x=60

Taking double differentiation, we get

Since double differentiation is positive, so At x=60 thousand players marginal cost is minimum

Mimimum Marginal cost

C(x) = 3600000000 -7200000 +7500

C(x)=$592,807,500