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#1046

**IEOR 3402: Assignment 4**

1. Nahmias 4.10.

2. Quarter-inch stainless-steel bolts are consumed in a factory at a fairly steady rate of 60 per week. The bolts cost the plant two cents each. It costs the plant $12 to initiate an order, and holding costs are based on an annual interest rate of 25 percent.

(a) Determine the optimal number of bolts for the plant to purchase and the time between placements of orders.

(b) What is the yearly holding and setup cost for this item?

3. Reconsider the bolt example in Problem 2. Suppose that although we have estimated demand to be 60 per week, it turns out that it is actually 120 per week (i.e., we have a 100 percent forecasting error).

(a) If we use the lot size calculated in the previous problem (i.e., using the erroneous demand estimate), what will the setup plus holding cost be under the true demand rate?

(b) What would the cost be if we had used the optimum lot size?

(c) What percentage increase in cost was caused by the 100 percent demand forecasting error? What does this tell you about the sensitivity of the EOQ model to errors in the data?

4. Consider the bolt example in Problem 2, assuming that the demand of 60 per week is correct. Now, however, suppose the minimum reorder interval is one month and all order cycles are placed on a power-of-two multiple of months (that is, one month, two months, four months, eight months, etc) in order to permit truck sharing with orders of other parts.

(a) What is the least-cost reorder interval under this restriction?

(b) How much does this add to the total cost?

(c) How is the effectiveness of powers-of-2 order intervals related to the result of the previous problem regarding the effect of demand forecasting errors?

5. * Nahmias, 4.17.

6. * In the EOQ model with planned backorders, suppose the parameters are λ = 1000, K = 60, h =0.75 and b =0.81. Compute the optimal policy and the optimal average cost (excluding cλ).

7. *Nahmias, 4.26.

8. * Nahmias, 4.30.

Please answer all the questions in attached documents.

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- Posted by: Orangecream
- Subjects: Math Environmental Law

Solution Details:
#1053

**1. The singular form of the word “dice” is “die”. Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What’s the probability of getting a three at the third time?**

Since the die has six sides and each instance of throwing the die is independent, it is merely a question of compounded AND probabilities : 1/6*1/6*1/6 = 1/216 = 0.004629629629…

**2. There are 30 table tennis balls in the box: 6 are green, 10 are red, and 14 are yellow. If you shake the box and then randomly select one ball from the box, what’s the probability that you will get a red one:**

10 / 30 = 1/3 of all the balls are red, therefore the probability of selecting a red ball is also 1/3.

**3. Rachel was flipping a coin with Jerry. She told jerry: “I am able to get all heads in two tosses.” Jerry laughed at her: “No, the probability of getting two heads at two tosses is only__”**

1/2*1/2 = 1/4

**4. Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would receive the free tickets. What’s the probability of Jennie and Alex both getting free tickets?**

This is an AND problem, so it is 10/20*10/20 = 1/2*1/2 = 1/4 = 0.25

**5. Laura and Melissa were playing dice. What the probability of Laura and Melissa both getting a 6?**

1/6*1/6 = 1/36

**6. In a statistics class with 36 students, the professor wanted to know the probability that at least two students share the same birthday. The probability will be___**

a. 0.1

**b. Much smaller than 0.1**

c. Much bigger than 0.1

d. Not possible

**7. If you throw a die for two times, what is the probability that you will get a one on the first throw or a o... **

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Solution Details:
#1053

A+ grade guaranteed! I always give g...

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**Tutormaster**

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