The estimated cost for a multitube cyclone system with a capacity of 60,000 cubic feet per minute is $450,000. (a) If the $200,000 actual cost for a 35,000 cubic feet per minute system was used in the cost-capacity equation, what was the value of the exponent? (b) What can be concluded about the economy of scale of the costs between the two systems?
What will be an ideal response?
(a) 450,000 = 200,000(60,000/35,000)^x
2.25 = 1.7143^x
log 2.25 = x log 1.7143
x = 1.504
(b) Since x > 1.0, there is dis-economy of scale, so that the percentage increase in cost is
greater than the percentage increase in size, which is the opposite of most situations.
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