| 請自選二類題作答，並請標示答類號。 |
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| 第一類： |
工程統計 |
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1. |
(10分) |
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An experiment was conducted in which two
types of engines, A and B, were compared. Gas mileage in miles per gallon
was measured. Fifty experiments were conducted using engine type A and
75 experiments were done for engine type B. The gasline used and other
conditions were held constant. The average gas mileage for engine A was
36 miles per gallon and the average for engine B was 42 miles per gallon.
Find a 96% confidence interval on μB – μA , where
μB and μA are population mean gas mileage for engines
B and A, respectively. Assume that the population standard deviations
are 6 and 8 for engines A and B, respectively.
Hint: z0.02 = 2.05. |
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2. |
(15分) |
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Prove that the mean and variance of the binomial distribution
b(x; n, p) are μ= np and  ,
respectively, where x is the binomial random variable, n
the Bernoulli independent trials, p the success probability, and
q=1-p . |
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3. |
(25分) The amounts of a chemical compound y, which dissolved
in 100 grams of water at various temperatures x, were recorded as follows: |
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| (a) |
(5分) |
Find the equation of the regression line. |
| (b) |
(5分) |
Evaluate s2 , the unbiased estimate of  . |
| (c) |
(5分) |
Construct a 99% confidence interval for α. |
| (d) |
(5分) |
Construct a 99% confidence interval for the average amount of
chemical that will dissolve in 100 grams of water at 50 ℃. |
| (e) |
(5分) |
Based on the repeated observations, test for linearity of regression.
Use a 0.05 level of significance. |
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Hint: t0.005=2.921 with ν=16 degrees of freedom.
f0.05=3.26 with 4 and 12 degrees of freedom. |
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| 第二類： |
作業研究 |
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1. |
(25分)一工廠欲生產A,B,C三種產品，此三種產品是由三種原料所組成，其相關資料如下: |
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Product
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Specification
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Selling price
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A
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Material 1: not more than 30% of total
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$8.50/unit
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Material 2: not less than 40% of total
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Material 3: exactly 20% of total
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B
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Material 1: Not more than 50% of total
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$7.00/unit
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Material 2: Not less than 10% of total
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Material 3: Exactly 10% of total
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C
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Material 1: not more than 70% of total
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$5.50/unit
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Material
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Units Available
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Cost per unit
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1
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3000
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$3.00
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2
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2000
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$6.00
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3
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1000
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$5.00
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將此問題寫成Linear Programming Model，不必求解。 |
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2. |
Given the following (one-step) transition matrix of a Markov
chain |
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| (a) |
(15分) |
Find the steady-state probabilities of the state of the Markov
chain. |
| (b) |
(10分) |
Starting from state 2, what is the probability that the process
will be in state 3 after two time unit? |
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| 第三類： |
計算機概論 |
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1. |
(15分) |
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| (a) |
Discuss the difference between Java and C# (5分). |
| (b) |
Discuss the difference between J2EE and .NET (10分). |
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2. |
(15分) Discuss the advantages and disadvantages
among traditional EDI, XML/EDI, and RosettaNet for business to business
(B2B) transactions. |
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3. |
(20分) An integer array X[n] is given with any size of N.
Write a program (You could choose one programming language from
the following languages: Basic, VB, VC, C, C++, C#, Java, Pascal, Fortran.
Specify your choice.) to |
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Separate the original array into two arrays Y[k] and Z[m], one
is for odd number, and the other is for even number; |
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Sort these two arrays by calling one sorting sub-program using
any sorting method (Specify your method.); |
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Find the sum of elements for each array; and |
| (d) |
Test your program with the following data: X[] = [ 22, 11, 14,
3, 36, 27, 37, 2, 45]. |
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| 第四類： |
案例分析 |
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(50分) Case Study: Buyer-seller networks interaction |
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In recent years, many industries have
developed a tiered supplier structure, resembles a pyramid. The original
equipment manufacturers (OEM), such as most manufacturers in Taiwan are
at the top of the pyramid. They often buy their products (mostly subassemblies)
from first tier suppliers (main suppliers). The main suppliers purchase
their subassemblies and components from second-tier suppliers (jobbers).
Jobbers are small companies that specialize in electro-mechanical activities. |
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Usually these process-manufacturers target their marketing
and sales strategies towards getting a favored status in relationship
with the OEMs. Nowadays some leading OEMs, through value chain analysis,
have tried to integrate the first-tier suppliers into their development
and operation processes. Often this leads to a situation where the OEM
actually will support its first-tier suppliers in their negotiations with
their second-tier suppliers and base material suppliers. |
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Questions: |
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| 1. |
What is the strengths (reasons of their success) of OEMs in Taiwan
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Discuss the requirements for a successful buyer-seller network. |
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What is customer value ? |
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How is customer value measured ? |
| 5. |
How does supply chain management contribute to customer value? |
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