OPIM Assignment 4
1. Cu = 24-11 = $13
Co = 11-7 = $4
Critical ratio = 13/(13+4) = 0.7647
μ = 30,000
σ = 10,000
Using normal distribution function (=norminv(0.7647,30000,10000)), the optimum order quantity is 37,216 jerseys to maximize profit.

2. Quantity = 32,000
First, we normalize the order quantity to find the z-statistic z=Q-μσ=32,000-25,00010,000=0.7
We then look up the standard normal loss function. The expected lost sale is given by. Lz=0.1429
Therefore, the expected lost sales = 10,000 * 0.1429 ≈ 1,429 Expected sales = 30,000 – 1,429 = 30,571 jerseys

3. First, we normalize the order quantity to find its z-statistic z=Q-μσ=28,000-20,00010,000=0.8
In-stock probability = normdist(0.8, 0, 1, 1) = 0.788145
Therefore, the probability of filling all demand is 0.788145

4. Quantity = 8,000
First, we normalize the order quantity to find the z-statistic z=Q-μσ=8,000-15,00010,000=-0.7
We then look up the standard normal loss function. The expected lost sale is given by. Lz=0.8429
Therefore, the expected lost sales = 10,000 * 0.8429 = 8,429 Expected sales = 15,000 – 8,429 = 6,571 jerseys
Expected leftover = 8000 – 6,571 = 1429 jerseys
Therefore, Nike has to sell 1,429 on discount

5. Cu = 16-11 = $5
Co = 9-7 = $2
Critical ratio = 5/(5+2) = 0.7143
μ = 40,000
σ = 10,000
Using normal distribution (=norminv(0.7143,40000,10000)), the optimum order quantity is 45660 jerseys in the first order to maximize profit.

6. Cu = 0.02-0.01 = $0.01
Co = 0.01-0 = $0.01
Critical ratio = 0.01/(0.01+0.01) = 0.5
μ = 300
σ = 75
Using normal distribution (=norminv(0.5,300,75)), the optimum order quantity is 300 million minutes from Vmail to minimize the expected capacity expense.

7. Q = 375
First, we normalize the order quantity to find the z-statistic z=Q-μσ=375-30075=1
We then look up the standard normal loss function. The expected lost sale is given by. Lz=0.0833
Therefore, the expected lost sales = 75 * 0.0833 = 6.2498...

...Week 4 Homework
Solutions: ProblemSet4
1. Determining Profit or Loss from an Investment. Three years ago, you purchased 150 shares of IBM stock for $88 a share. Today, you sold your IBM stock for $103 a share. For this problem, ignore commissions that would be charged to buy and sell your IBM shares.
a. What is the amount of profit you earned on each share of IBM stock? The profit on each share of IBM...

...FIN 350
Prof. Porter
ProblemSet4
1. Describe what happens to the total risk of a portfolio as the number of securities is increased. Differentiate between systematic risk and unsystematic risk and explain how total risk and systematic risk are measured.
As the number of securities increases, the total risk of the portfolio decreases. This decrease occurs due to the benefits of diversification which is the process of acquiring a portfolio...

...PROBLEMSET4
1) Consider the following utility functions, where W is wealth:
(a) U (W ) = W 2
1
(b) U (W ) =
W
(c) U (W ) = −W
(d) U (W ) = W
(e) U (W ) = ln(W )
(f) U (W ) =
W 1−γ
, with γ = 2
1−γ
How likely are each of these functions to represent actual investor preferences? Why?
2) Suppose investors have preference described by the following utility function
with A > 0:
U = E(r) − 1 Aσ 2
2
Each investor has to choose...

...4. What combination of the two goods below allows you to maximize your utility with a budget constraint of $14? Show how you arrived at your conclusion in the space provided below. Place your final answers on the lines at the bottom of this page.
PRICE = $0.50 per pint
|Bottles of glue |Total Utility (Utils) |
|1 |15 |
|2 |23 |
|3 |30...

..._________________________________ PROBLEMSET4
1. What combination of the two goods below allows you to maximize your utility with a budget constraint of $14? Show how you arrived at your conclusion in the space provided below. Place your final answers on the lines at the bottom of this page.
PRICE = $0.50 per pint
Pints of Butter Beer
Total Utility (Utils)
1
15
2
23
3
30
4
35
5
38
6
40.5
PRICE = $2.00 per box
Boxes of Bertie...

...ECE 302
ProblemSet 9
Fall 2013
The following problems have been selected from the course text.
4.78 In a large collection of wires, the length of a wire is X, an exponential random variable with mean
5π cm. Each wire is cut to make rings of diameter 1 cm. Find the probability mass function for the
number of complete rings produced by each length of wire.
4.85 The exam grades in a certain class have a Gaussian pdf with mean m and standard...