1. You have been hired as a consultant to a legal firm. Part of your assignment

Question

1. You have been hired as a consultant to a legal firm. Part of your assignment is to determine the size of a rotary vacuum drum filter purchased in 1984 (CEPCl 323) before computerization of records. The filter was replaced every 16 years, and the sizes have changed due to plant capacity changes. You have the information in Table 1 below. Estimate a. The equipment cost exponent b. The original capacity of this filter Table 1. Cost Data for Problem 1 Year Filter area, Purchased Cost 1984 $49,600.00 $67,400.00 2016 | 110 |$97,100.00 2 2000 100

Explanation / Answer

Part a

(Cost of filter purchased in 2000 / Cost of filter purchased in 2016) = (capacity of filter purchased in 2000 / capacity of filter purchased in 2016)^n

($67400 / $97100) = (100/110)^n

0.694 = 0.909^n

Take natural logarithm on both sides

ln 0.694 = n ln(0.909)

n = 3.83

Part b

Let original capacity of filter = X

(Cost of filter purchased in 2000 / Cost of filter purchased in 1984) = (capacity of filter purchased in 2000 / capacity of filter purchased in 1984)^n

($67400 / $49600) = (100/X)^3.83

1.3588 = (100/X)^3.83

Take natural logarithm on both sides

ln 1.3588 = 3.83 ln (100/X)

ln (100/X) = 0.08

100/X = 1.083

X = 92.31 m2

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