The total cost (in hundreds of dollars) to produce xx units of a product is C(x)=8x−16x+7C(x)=8x−16x+7

Accounting Dec 08, 2020

The total cost (in hundreds of dollars) to produce xx units of a product is C(x)=8x−16x+7C(x)=8x−16x+7. Find the average cost for each of the following production levels.

a) 40 units

b) xx units

c) Find the marginal average cost function.

Expert Solution

A) The average cost of producing 40 units will be :

C(40)40=8∗40−16∗40+740=0.03229C(40)40=8∗40−16∗40+740=0.03229

B) We need to find the average cost function. This will be just be the total cost function divided by the number of units produced, x.

¯C(x)=8x−16x+7x=8x−1x(6x+7)=8x−16x2+7xC¯(x)=8x−16x+7x=8x−1x(6x+7)=8x−16x2+7x

C) The marginal average cost function will be the derivative of the average cost function found above.

¯C′(x)=ddx8x−16x2+7xUsing the quotient rule,¯C′(x)=(6x2+7x)∗8−(8x−1)∗(12x+7)(6x2+7x)2=−48x2−12x−7x2(6x+7)2

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