Find the number of units x that produces the minimum average cost per unit C in the given equation. C = 0.001×3 + 4x + 1024?

2 Answers

• C = 0.001x³ + 4x + 1024

  unit cost f(x) = C/x = 0.001x² + 4 + 1024/x

  f'(x) = 0.002x - 1024/x²

  Set first derivative to zero

  0.002x - 1024/x² = 0

  0.002x = 1024/x²

  0.002x³ = 1024

  x³ = 512·10³

  x = ∛512·10 = 80

• average cost per unit A(x) = C(x)/x = 0.001x^2 + 4 + (1024/x)

  dA/dx=0

  solve for x