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 (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?

Answer 1

Answer:

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

Answer 2

A) The number of players should be 80

B)  The minimum marginal cost is $1,400

Calculation of no of players & the marginal cost:

a.

Given that,

C(x) = x² - 160x + 7,800

Here b= -160 ; a = 1

Now

x = - (-160) / 2 = 80    

2.

Now

C (80) = 80² - (160 x 80) + 7,800

= 1,400

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