Question

Suppose that c (x )equals 2 x cubed minus 12 x squared plus 23 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Answer 1

x = 4 units

Explanation:

Data provided in the question:

c(x ) = 2x³ - 12x² + 23,000

Now,

For point of maxima or minima, differentiating the above equation with respect to number of items 'x'

c'(x) = 3(2x²) - 2(12x) + 0

or

c'(x) = 3(2x²) - 2(12x)

for point of maxima or minima put c'(x) = 0

Thus,

3(2x²) - 2(12x) = 0

or

6x² - 24x = 0

or

x² - 4x = 0

or

x(x - 4) = 0

or

x = 0 and, x = 4

Since,

The quantity cannot be zero

Therefore,

production level that will minimize the average cost of making x items is x = 4 units