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 (x )equals x squared minus 160 x plus 7800. a. how many players should be produced to minimize the marginal cost? b. what is the minimum marginal cost?

The answers are:

A) 80,000 MP3 players

B) $1,400

Explanation:

To solve the following equation we must : C(x) = x² - 160x + 7,800

Step 1)

Since this is a quadratic function (parabola), the minimum value for x= -b/ 2a

where b= -160 ; a = 1

x = - (-160) / 2 = 80    

THEY SHOULD PRODUCE 80,000 MP3 PLAYERS

Step 2)

Then we replace x = 80

C (80) = 80² - (160 x 80) + 7,800 = 1,400

THE MINIMUM MARGINAL COST FOR PRODUCING 1,000 MP3 PLAYERS IS $1,400

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