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A promoter proposes to double a plant's capacity and assumes the capital cost will double too.

What should be pointed out?

  • A.Cost scales to a power near 0.6, not linearly
  • B.Cost will more than double
  • C.Cost is independent of capacity
  • D.Cost scales linearly only above 20 t/h

Answer: A

Correct answer: Cost scales to a power near 0.6, not linearly

By the six-tenths rule, \(C_2 = C_1 (Q_2/Q_1)^{0.6}\), so doubling the capacity multiplies cost by \(2^{0.6} = 1.52\) - about half again. The economy of scale arises because a vessel’s cost follows its surface while its capacity follows its volume.

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