Assume that it costs a company approximately c(x) = 484,000 + 160x + 0.001x2 dollars to manufacture x units of a device in an hour at one of their manufacturing centers. how many devices should be manufactured each hour to minimize average cost? units what is the resulting average cost of a device? $ how does the average cost compare with the marginal cost at the optimal production level? find how much they differ. $

How many devices should be manufactured each hour to minimize average cost?

21,909

What is the resulting average cost of a device?

$204

How does the average cost compare with the marginal cost at the optimal production level?

The average cost exceeds the marginal cost in  $0.18

Step-by-step explanation:

The average cost A(x) equals the total cost C(x) divided by the number x of units produced in a given period. So

How many devices should be manufactured each hour to minimize average cost?

Taking the first derivative A'(x) with respect to x

The points where A'(x) = 0 (critical points) are

So, x=21,908.9023 and x = -21,9023 are the two critical points.

To find out which one is a minimum we take the second derivative A''(x)

and A''( 21,908.9023) > 0 , so x = 21,908.9023 is a minimum.

Given that x must be an integer  

x = 21,909

is the number of units that minimizes the average cost.

What is the resulting average cost of a device?

It would be A(21,909):

How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ.

The marginal cost is  

C'(x) = 160 + 0.002x

hence

C'(21,909) = 160 + 0.002(21909) = $203.82

and the average cost exceeds the marginal cost in

204 - 203.82 = $0.18

at the optimal  production level.

step-by-step explanation:

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step-by-step explanation: