1
Stochastic Processes,
Theory for Applications
Solutions to Selected Exercises
R.G.Gallager
October 5, 2014
The complete set of solutions is available to instructors teaching this course. Contact
Cambridge Press at www.Cambridge.org.
The solutions here o

Source:
Vancouver
San Francisco
Toronto
Los Angeles
New York
Source:
Source:
84 in-flight meals
656 in-flight meals
Due to the volume of passenger bookings, the airline needs to purchase
6,000 in-flight meals.
Six possible suppliers have submitted their q

Master Yu
Master Yu is planning to get a franchise to sell a unique recipe of Turon. The franchise fee is P 120,000 to be paid in 24 equal monthly
space rental of P 10,000 per month which already includes his projected electricity and water consumption. H

Fixed Cost
Problem
Mansci s05
Ablaza, Hebreo, Jusay,
Murakami, Tan
Source:
BOEING777
Vancouver
San Francisco
Toronto
Los Angeles
New York
Source:
BOEING777
= 10 seats
42 BUSINESS CLASS SEATS
= 10 seats
328 ECONOMY CLASS SEATS
Source:
BOEING777
84 in-fligh

Source:
Vancouver
San Francisco
Toronto
Los Angeles
New York
Source:
Source:
84 in-flight meals
656 in-flight meals
Due to the volume of passenger bookings, the airline needs to purchase
6,000 in-flight meals.
Six possible suppliers have submitted their q

SOLVER TEMPLATE
Case/Problem Name:
25-Jun
Note: Fill in only cells highlighted in yellow
Airline Meals
Problem Objective
Decision Variable ID
Quantity (leave blank)
Unit coefficients
Total Objective
Constraint Coefficients
1 Total Meals
2 Min Supplier 1
3

General and Admin Cost
40%
TABLE 1
A
B
C
D
E
F
G
H
J
K
L
M
ACTIVITY
Move in machinery/equipment
Excavate primary shaf
Excavate secondary shafs
Excavate trenches
Excavate tunnel
Backfill (trenches only)
Pipelaying in trenches
Pipelaying in tunnel
Pour conc

Fixed Cost Models
An airline needs to determine how best to meet its needs for in-flight meals on one of its
international flights for the coming month. Based on anticipated passenger bookings,
the airline must purchase 6,000 meals for the coming month. S

Chapter 3: Demand, Supply, and Equilibrium Prices
Chapter 4: Demand and Supply Applications
The following graph represents the market for wheat. The equilibrium price is $20 per bushel
and the equilibrium quantity is 14 million bushels.
o
Explain what wil

CHAPTER 6 Problem 7
Assume that Mei has $100 per month to divide between dinners at a Chinese restaurant and evenings at
Zanzibar, a local pub. Assume that going to Zanzibar costs $20 and eating at the Chinese restaurant costs
$10. Suppose Mei spends two

Applied Math
Chapter 8: Markups and Markdowns Perishables and Breakeven Analysis
1
Formula
Markups Based on Cost
Notes
Selling Price (P) = Cost (C) + Markup (M)
2
a.
P = C * (1 + Percent Markup on Cost (RC)
a. Calculating Selling Price when you know
Cost

First Question on slide 17:
Try compounding P10,000 annually, semianually, quarterly, monthly, daily at a
rate of 5% per annum. What are the effective rates here?
Period
No of
periods (N)
Interest
rate per
period (R)
Principal =
10000
Interest
(FV-PV)
APY

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Figure 1.2 Correlations between lattice observations Z(si) and the average of the nearest neighbors for lattice
arrangements shown in Figure 1.1.
Here, Z denotes the attribute we observe, for example, yield, conce

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Page 2
Example 1.1 A drug company is interested in testing the uniformity of its buffered aspirin tablets for quality control
purposes. A random sample of three batches of aspirin tablets is collected from each of the co

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Page 4
Similarly, in the longitudinal case, the observations from different subjects can be collected into a single vector,
and model (1.1) can be written as
Y=Xl+e,
(1.3)
where Xl is a stacking of X1, X2, , Xn, and e is

Applied Math
Multi-Product Breakeven Point
1
Contribution Margin = Amount remaining after variable costs
are deducted from sales amount
Contribution Margin Ratio = Contribution Margin expressed
as a percentage of sales
10%
Overall CM Ratio = Total CM / To

Practice Problems
Breakeven Point
1
1. Master Yu is planning to get a franchise to sell a unique recipe of turon. The
franchise fee is P 120,000 to be paid in 24 equal monthly installments at zero
interest. To operate, he needs two crew members with a com

SBEP
Applied Math
Contact Information
Manuel A. Tenmatay
[email protected]
0917- 837-4570
3
Course Title:
Applied
Mathematics
Textbook:
Practical Business
Math Procedures
(11th edition)
by Jeffrey Slater
(McGraw Hill)
Course Contents:
Application of mat

Single Transactions
Time Value of Money
Chapter 7 8 , 10 13
Interest on transactions is an amount that is charged for the use of somebody elses money
You borrow P30,000, to be paid one year after , at an interest rate of 8% per
year.
P
MV
One year
P = Pr

Practice Problems
Discounts Pricing 1
Practice Problem # 1
Kikos Bake Shop bakes 800 loaves of
bread per week at a cost of P70 each.
A mark up of 70% on cost is added in
setting up the selling price. Based on
experience, Kiko knows that 20 % of
the bread

Practice Problems Set 2
Time Value of Money
Problem 1
Two years ago, you bought a new sports car
with a P1.2 million bank loan at an interest
rate of 9 % per year compounded monthly.
The loan was to be paid in 48 months. After
24 months of payment, you d

Practice Problems Set 1
Time Value of Money
Problem 1
1. A loan of Php 500,000 is due 5 years from
today. (a) The borrower wants to make annual
deposits at the end of each year into a sinking
fund that will earn interest at an annual rate of
8%, compounde

Doing Business
Chapter 7 & 8
1
Get Discounts
on purchases
Buy on credit
or pay in cash
for more
discounts
Put Markup
on sales
Gain Profit
2
Payment = List Price Trade Discounts Cash Discounts + Freight
(1) Trade Discounts: Single
Chain
(2) Cash Discounts:

Interests on Transactions
Chapter 10 13
PV & FV of Annuities
An engineer deposits P1,000 in a savings account at the
end of each year for 5 years. How much money can he
withdraw at the end of 5 years if the bank pays interest
at the rate of 6% p.a. compou

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Page 51
models with nugget effect from consideration and reflects the sentiment that only the study of mean square
continuous processes is worthwhile.
Mean square continuity by itself does not convey much about the smoo