Question

The total cost (in dollars) of manufacturing x auto body frames is C(x) = 50,000+ 900x. 

(A) Find the average cost per unit if 400 frames are produced. 

(B) Find the marginal average cost at a production level of 400 units.

(C) Use the results from parts (A) and (B) to estimate the average cost per frame if 401 frames are produced. 

(A) If 400 frames are produced, the average cost is $_______  per frame.  

Answer 1

A.

Given,

TC = 50,000 + 900x

Now, given (x = 400)

TC = 50,000 + 900 × 400

      = 50,000 + 360,000

      = 410,000

Hence,

Average cost (AC) = TC / x

                               = 410,000 / 400

                               = 1,025 (Answer)

B.

AC equation should be established first.

Given,

TC = 50,000 + 900x

AC = TC / x

       = (50,000 + 900x) / x

       = 50,000/x + 900

Marginal AC = Derivative of AC with respect to x

                        = (d/dx) [50,000/x + 900]

                        = - 50,000/x^2 + 0

            = - 50,000/x^2

Marginal AC (x = 400) = - 50,000 / 400^2

                                    = - 50,000 / 160,000

                                    = - 0.3125 (Answer)

Since it is negative, the marginal AC reduces.

C.

AC = TC / x

       = (50,000 + 900x) / x

       = 50,000/x + 900

Now, (x = 401) should be placed in the equation.

AC = (50,000 / 401) + 900

       = 124.69 + 900

       = 1,024.69