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)=x^2-100x+8300. (a). How many players should be produced to minimize the marginal cost? and (b). What is the minimum cost??
If you take Calculus marginal is the derivative, the value of change at a point(margin).
C( X) = X2 - 100X + 8300
a) This is a quadratic function, the minimum value is @ - b/ 2a:
- ( -100) /2 = 50
C( 50) = (50) 2 - 100(50) + 8300 = 5800
Another way, using Calculus:
a) dC/dx = 2x - 100 =50