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.

x = 4 units

Step-by-step 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

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

answer: its the third option.

step-by-step explanation:

i just took the test.