Answer:
50 units
Step-by-step explanation:
Find the number of units x that produces the minimum average cost per unit C in the given equation.
C = 0.001x³ + 5x + 250
unit cost f(x) = C/x
= 0.001x³/x + 5x/x+ 250/x
f(x) = 0.001x² + 5 + 250/x
f'(x) = 0.002x - 250/x²
We equate the first derivative to zero
0.002x - 250/x² = 0
0.002x = 250/x²
Cross Multiply
0.002x × x² = 250
0.002x³ = 250
x³ = 250/0.002
x³ = 125000
x = 3√(125000)
x = 50 units
Therefore, the number of units x that produces the minimum average cost per unit C is 50 units.
