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# 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 ...

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??

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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
b)
C( 50) = (50) 2 - 100(50) + 8300 = 5800

Another way, using Calculus:

a)  dC/dx =  2x - 100 =50

4.9 4.9 (229 lesson ratings) (229)
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The Marginal cost is found by taking the derivative of the cost equation.

C(x) = x^2 - 100x + 8300

C'(x) = 2x - 100

This curve will have a minimum since it's a parabola that is concave up.

2x - 100 = 0

2x = 100

x = 50

50,000 mp3 players should be made to minimize the marginal cost

The minimum cost will be 50^2 - 100*50 + 8300 = \$5800
Brad M. | Summer Online Finance Specialist: WACC NPV DCF TVM YTMSummer Online Finance Specialist: WACC ...
4.9 4.9 (233 lesson ratings) (233)
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Hey Kevin -- at a minimum, the slope of the trough is zero ... take dC(X)/dX =0 ...

a) 2x -100 =0 ... x= 50 ==> produce 50k mp3 players
b) C(50) = 50*50 less 5k plus 8300 = 5800 min cost at x= 50 ... Best wishes, sir  :)