MSE 604 CH-12
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School
California State University, Northridge *
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Course
604
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
3
Uploaded by ChiefHawkPerson1087
California State University –
Northridge Department of Manufacturing Systems Engineering and Management HomeWork #12 MSE 604 –
Engineering Economy and Financial Analysis Fall: 2023 Professor: Ahmad R. Sarfaraz, Ph.D. Group Members: 1) Furkhan Faridi Mohammed 2)
Meer Shoaib Ali Hashmi 3)
Rohit Alex Oddi 4)
Gouse Mohiuddin Shaik
12-2. A bridge is to be constructed now as part of a new road. An analysis has shown thattraffic density on the new road will justify a two-lane bridge at the present time. Because of uncertainty regarding future use of the road, the time at which an extra two lanes willbe required is currently being studied. The estimated probabilities of having to widen thebridge to four lanes at various times in the future are as follows: The present estimated cost of the two-lane bridge is $2,000,000. If constructed now, the four- lane bridge will cost $3,500,000. The future cost of widening a two-lane bridge will be an extra $2,000,000 plus $250,000 for every year that widening is delayed. If money can earn 12% per year, what would you recommend? Solution: Build the 4−lane
bridge now: PW = −$3,500,000
Build 2−lane
bridge now, add two lanes later: Expansion year K PW of Expansion Expenses 3 −
[$2,000,000 + (3) ($250,000)] (P/F,12%,3) = −
$1,957,450 4 −
[$2,000,000 + (4) ($250,000)] (P/F,12%,4) = −
$1,906,500 5 −
[$2,000,000 + (5) ($250,000)] (P/F,12%,5) = −
$1,844,050 6 −
[$2,000,000 + (6) ($250,000)] (P/F,12%,6) = −
$1,773,100 E(PW) = −
$2,000,000 −
$1,957,450(0.1) −
$1,906,500(0.2) −
$1,844,050(0.3) −$1,773,100(0.4)
= −$3,839,500
Decision: The four−lane bridge
should be built now. 12-3. A new snow making machine utilizes technology that permits snow to be producedin ambient temperature of 70 degrees Fahrenheit or below. The estimated cash flows forthe ski resort contemplating this investment are uncertain as shown below (note: pr. = probability).
The machine is expected to have a useful life of 12 years, and the MARR of the ski resortis 8% per year. What is the expected present worth of this investment? Solution: Expected revenues = $140,000 (0.6) + $135,000 (0.4) = $138,000 Expected expenses = $60,000 (0.6) + $50,000 (0.4) = $56,000 Expected salvage value = $40,000 (0.5) + $35,000 (0.5) = $37,500 Expected PW (8%) = -$120,000 + ($138,000 - $56,000) (P/A, 8%, 12) + $37,500 (P/F, 8%, 12) = $120,000 + $617,960 + $14,891 = $512,851 This is a attractive investment. 12-15. In an industrial setting, process steam has been found to be normally distributed with an average value of 25,000 pounds per hour. There is an 80% probability that steamflow lies between 20,000 and 30,000 pounds per hour. What is the variance of the steam flow? Solution: P(20000 <x<30000) = 0.8 From the normal probability tables (App. E): z-value = 0.84162 From the normal probability tables (App. E): 1.28 = (X - μ)
/ σ
= (30,000 - 25,000) / σ
= 5,000 / σ
so σ
= 3,906.25 pounds per hour and the variance = σ²
= 15.26 x 10⁶
(lbs/hr)²
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