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

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