Question

8. Suppose the total cost function is as follows: TC= x^3/3 -x^2+11x

Answer 1

At 1.5 the average total cost is a minimum and the total cost will be 10.25 where the TC = total cost; x = output (in 1,000 units)

What are maxima and minima?

Maxima and minima of a function are the extremes within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.

We have a total cost function:

TC = x³/3 - x² + 11x

Average total cost:

$\rm F\left(x\right)=\dfrac{\left(\dfrac{x}{3}^3-\:x^2\:+\:11x\right)}{x}$

Differentiating with respect to x and equating to x

d(F(x))/dx = 0

We will get:

x = 1.5

F'(1.5) >  0

At 1.5 the average total cost is a minimum.

Thus, at 1.5 the average total cost is a minimum and the total cost will be 10.25 where the TC = total cost; x = output (in 1,000 units)

Learn more about the maxima and minima here:

brainly.com/question/6422517

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