A lot of companies use the marginal cost function for their business models to determine the production level to minimize total costs. As we all know, if C (x) represents the total cost of producing x units of a product, then the average cost per unit at this production C(x) level is . Let assume C (x) is differentiable on all x > 0. This implies that the average cost function is also differentiable for all x > 0 since C(x) can be written as C (x) · - , and both C (x) and - are differentiable for all x > 0. Suppose you go to an interview and the chairman of the interview committee gives you the following questions: In our company , we use marginal cost to determine the production level to minimize the costs. However, there is another useful model in business, the average cost function, that we also track. 1. Is it true or not that the marginal cost C ' (x) is equal to the average cost at the critical points of the average cost function? Please elaborate and explain to us. 2. This year, the costs at the x production level is expected to be C (x) = 16000 + 200x + 4xž , in dollars. What production level would you advise us to hold in order to minimize the average cost per item? %3D
A lot of companies use the marginal cost function for their business models to determine the production level to minimize total costs. As we all know, if C (x) represents the total cost of producing x units of a product, then the average cost per unit at this production C(x) level is . Let assume C (x) is differentiable on all x > 0. This implies that the average cost function is also differentiable for all x > 0 since C(x) can be written as C (x) · - , and both C (x) and - are differentiable for all x > 0. Suppose you go to an interview and the chairman of the interview committee gives you the following questions: In our company , we use marginal cost to determine the production level to minimize the costs. However, there is another useful model in business, the average cost function, that we also track. 1. Is it true or not that the marginal cost C ' (x) is equal to the average cost at the critical points of the average cost function? Please elaborate and explain to us. 2. This year, the costs at the x production level is expected to be C (x) = 16000 + 200x + 4xž , in dollars. What production level would you advise us to hold in order to minimize the average cost per item? %3D
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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Transcribed Image Text:A lot of companies use the marginal cost function for their business models to determine
the production level to minimize total costs. As we all know, if C (x) represents the total
cost of producing x units of a product, then the average cost per unit at this production
Let assume C (x) is differentiable on all x > 0 . This implies that the
C(x)
level is
average cost function is also differentiable for all x > 0 since
C(x)
can be written as
C (x) · - , and both C (x) and
are differentiable for all x > 0.
Suppose you go to an interview and the chairman of the interview committee gives you
the following questions:
In our company , we use marginal cost to determine the production level to minimize the
costs. However, there is another useful model in business, the average cost function, that
we also track.
1. Is it true or not that the marginal cost C '(x) is equal to the average cost at the
critical points of the average cost function? Please elaborate and explain to us.
2. This year, the costs at the x production level is expected to be
3
C (x) = 16000 + 200x + 4xž , in dollars. What production level would
you
advise
us to hold in order to minimize the average cost per item?
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