The production level that would minimize the average cost per item of making x items is x = 12
How to solve for the production level
We have Cx = x3 - 24x2 + 30,000x
divide through the equation by x, this would give us
c = x² - 24x + 30,000
we have to take the first derivative of this
so we would have
2x - 24= 0
From the equation above we have
2x = 24
divide through by 2
x = 24/2
x = 12
The production level that would minimize the average cost per item of making x items is x = 12
Complete question
Suppose c(x) = x3 - 24x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost per item of making x items.
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