A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
13th Edition
ISBN: 9780135183885
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 9.4, Problem 1MC
The terms Fundamental Counting Principle, permutations, and combinations are all used to work with counting problems. In your own words, explain how all these terms are related and how they are used.
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(c) Describe the distribution plan and show the total distribution cost.
Optimal Solution
Amount
Cost
$ 2000
Southern-Hamilton
200
Southern-Butler
$
Southern-Clermont
300
4500
Northwest-Hamilton
200
$2400
Northwest-Butler
200
$3000
Northwest-Clermont
$
Total Cost
ક
(d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units.
(i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier.
Distribution Plan with Southern Gas
Amount
Southern-Hamilton
$
Cost
×
Southern-Butler
x
$
Southern-Clermont
300
$ 4500
Northwest-Hamilton
64
x
Northwest-Butler
$
×
Northwest-Clermont 0
$0
Total Cost
$
(ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier.
Distribution Plan with Northwest Gas
Southern-Hamilton
Southern-Butler
0
Southern-Clermont
Northwest-Hamilton
Northwest-Butler
Northwest-Clermont
Total Cost
Amount
×
x
x
+7
$0
Cost
×
$
×
$
×
+4
$
-/+
$
×
×
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows.
Warehouse
Plant
Capacity
1
2
1
4
7
450
2
8
5
600
3
5
6
380
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows.
Customer
Warehouse
1
2 3
1
6
4
8
2
3
6
7
7
Demand
300 300 300 400
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
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(b) Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9. Express your answers in the form x;;, where x,; represents the number of units shipped from
node i to node j.)
Min 4x14+8x24+5x34+7x15 +5x25…
A linear programming computer package is needed.
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its
rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and
Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are…
Chapter 9 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 9.1 - Prob. 1MCCh. 9.1 - Prob. 2MCCh. 9.1 - Prob. 3MCCh. 9.1 - Prob. 4MCCh. 9.1 - Prob. 5MCCh. 9.1 - Prob. 6MCCh. 9.1 - If possible, for each of the following letters,...Ch. 9.1 - Prob. 8MCCh. 9.1 - Jose claims that if the following spinner is spun...Ch. 9.1 - Zoe is playing a game in which she draws one ball...
Ch. 9.1 - Ian and Sophia flip a fair coin ten times and...Ch. 9.1 - A certain game has four mutually exclusive...Ch. 9.1 - Prob. 13MCCh. 9.1 - A student observes the following spinner and...Ch. 9.1 - Prob. 15MCCh. 9.1 - Prob. 16MCCh. 9.1 - Prob. 17MCCh. 9.1 - Board games that use dice sometimes give children...Ch. 9.1 - Suppose the figure in exercise 14 is a is a...Ch. 9.1 - On the School Book Page on page 501, complete the...Ch. 9.1 - Mark has nine shirts in his closet as shown. If...Ch. 9.1 - Ms. Livingstons class spins the arrow on the...Ch. 9.1 - Lori has a choice of two spinners. She wants the...Ch. 9.1 - Each of the 6 faces of a fair cube is painted red,...Ch. 9.1 - Prob. 5NAEPCh. 9.1A - Consider the experiment of drawing a single card...Ch. 9.1A - The experimental probability of rolling a 4 on a...Ch. 9.1A - Each letter of the alphabet is written on a...Ch. 9.1A - The spinner shown is spun. Find the probability of...Ch. 9.1A - A card is selected from a ordinary deck of 52...Ch. 9.1A - Suppose a drawer contains six black socks, four...Ch. 9.1A - Prob. 7ACh. 9.1A - According to a weather report, there is a 30...Ch. 9.1A - A set of dolls is in a packing crate: 17 with...Ch. 9.1A - The plays generally considered the tragedies by...Ch. 9.1A - Prob. 11ACh. 9.1A - Prob. 12ACh. 9.1A - A calculus class is composed of 35 men and 45...Ch. 9.1A - A box contains five white balls, three black balls...Ch. 9.1A - Prob. 16ACh. 9.1A - If you flipped a fair coin 15 times and got 15...Ch. 9.1A - A witness identified all the digits on a license...Ch. 9.1A - Prob. 20ACh. 9.1A - If A and B are mutually exclusive, P(A)=0.3, and...Ch. 9.1A - How many times would you except to obtain a 4 on a...Ch. 9.1B - Prob. 1ACh. 9.1B - Prob. 2ACh. 9.1B - In each of the following scenarios, sketch a...Ch. 9.1B - Prob. 4ACh. 9.1B - Prob. 5ACh. 9.1B - Prob. 6ACh. 9.1B - Prob. 7ACh. 9.1B - Prob. 8ACh. 9.1B - Prob. 9ACh. 9.1B - Prob. 10ACh. 9.1B - Prob. 11ACh. 9.1B - Prob. 12ACh. 9.1B - Prob. 13ACh. 9.1B - Prob. 14ACh. 9.1B - Prob. 17ACh. 9.1B - What is the probability of choosing a continent at...Ch. 9.1B - Prob. 20ACh. 9.1B - Prob. 21ACh. 9.1B - How many times would you except to obtain a 6 on a...Ch. 9.2 - Six fair dice are thrown at the same time. If...Ch. 9.2 - A witness to a crime observed that the criminal...Ch. 9.2 - You are given three white balls, one red ball, and...Ch. 9.2 - Prob. 4MCCh. 9.2 - Prob. 5MCCh. 9.2 - Make up a game in which the players have an equal...Ch. 9.2 - How can the faces of two cubes be numbered so that...Ch. 9.2 - Mathematical Connections Design a pair of...Ch. 9.2 - An experiment consists of tossing a fair coin...Ch. 9.2 - Prob. 11MCCh. 9.2 - A student would like to know the difference...Ch. 9.2 - In response to the question, If a fair die is...Ch. 9.2 - A student is not sure when to add and when to...Ch. 9.2 - There are two boxes with different-colored balls....Ch. 9.2 - Alberto is to spin the spinners shown and compute...Ch. 9.2 - Match the following phrase to the probability that...Ch. 9.2 - A date in the month of April is chosen at random....Ch. 9.2 - Three men were walking down a street talking when...Ch. 9.2 - A roulette wheel has 38 slots around the rim; 36...Ch. 9.2 - If the roulette wheel in exercise 21 is spun 190...Ch. 9.2 - Prob. 1NAEPCh. 9.2 - Prob. 2NAEPCh. 9.2 - Prob. 3NAEPCh. 9.2 - National Assessment of Educational Progress NAEP...Ch. 9.2A - Assessment A pair of fair dice is rolled. Find the...Ch. 9.2A - Assessment a. A box contains three white balls and...Ch. 9.2A - Prob. 4ACh. 9.2A - An executive committee consisted of 10 members: 4...Ch. 9.2A - Assume the probability is 12 that a child born at...Ch. 9.2A - Prob. 7ACh. 9.2A - Assessment You roll a die twice and take the...Ch. 9.2A - Prob. 9ACh. 9.2A - If a person takes a five-question true-false test,...Ch. 9.2A - Assessment Rattlesnake and Paxson Colleges play...Ch. 9.2A - Consider the following dartboard where all...Ch. 9.2A - Prob. 13ACh. 9.2A - There are 40 employees in a certain firm. We know...Ch. 9.2A - Prob. 15ACh. 9.2A - When you toss a quarter 4 times, what is the...Ch. 9.2A - Prob. 17ACh. 9.2A - Prob. 18ACh. 9.2A - Prob. 19ACh. 9.2A - A bag contain 3 blue marbles, 4 red marbles, and 3...Ch. 9.2A - Assessment You roll a die twice. a. The sum of the...Ch. 9.2A - Prob. 22ACh. 9.2A - Prob. 23ACh. 9.2A - Prob. 24ACh. 9.2A - Following are three boxes containing balls. Draw a...Ch. 9.2B - Prob. 1ACh. 9.2B - Prob. 3ACh. 9.2B - Prob. 4ACh. 9.2B - Prob. 5ACh. 9.2B - Prob. 6ACh. 9.2B - Prob. 11ACh. 9.2B - Prob. 13ACh. 9.2B - Prob. 14ACh. 9.2B - A husband and wife discover that there is a 10...Ch. 9.2B - Prob. 16ACh. 9.2B - Prob. 17ACh. 9.2B - Prob. 21ACh. 9.2B - Prob. 22ACh. 9.2B - Assessment At her favorite coffee shop, Ashaunte...Ch. 9.2B - Assessment In box number 1, there are 4 blue...Ch. 9.3 - Prob. 1MCCh. 9.3 - Prob. 2MCCh. 9.3 - A game involves tossing two coins. A player wins...Ch. 9.3 - Prob. 4MCCh. 9.3 - Suppose we toss two fair coins. Design a fair game...Ch. 9.3 - Prob. 8MCCh. 9.3 - Prob. 9MCCh. 9.3 - At the beginning of this season, the odds listed...Ch. 9.3 - Prob. 11MCCh. 9.3 - Prob. 13MCCh. 9.3 - Prob. 14MCCh. 9.3 - Prob. 15MCCh. 9.3 - Prob. 16MCCh. 9.3 - Prob. 17MCCh. 9.3 - Prob. 18MCCh. 9.3 - Prob. 19MCCh. 9.3 - Prob. 20MCCh. 9.3 - Prob. 21MCCh. 9.3 - From a sack containing seven red marbles, eight...Ch. 9.3 - Prob. 23MCCh. 9.3 - Prob. 24MCCh. 9.3 - Prob. 25MCCh. 9.3 - Prob. 26MCCh. 9.3A - Could we use a thumb tack to simulate the birth of...Ch. 9.3A - Prob. 2ACh. 9.3A - Prob. 4ACh. 9.3A - Prob. 5ACh. 9.3A - Prob. 6ACh. 9.3A - Pick a block of two digits from the random-number...Ch. 9.3A - Prob. 8ACh. 9.3A - Prob. 10ACh. 9.3A - Prob. 11ACh. 9.3A - Prob. 12ACh. 9.3A - If the probability of a boys being born is 12, and...Ch. 9.3A - If the odds against Deborahs winning first prize...Ch. 9.3A - If the probability of the event that a randomly...Ch. 9.3A - Prob. 16ACh. 9.3A - Prob. 17ACh. 9.3A - Prob. 18ACh. 9.3A - Prob. 19ACh. 9.3A - Prob. 20ACh. 9.3A - Prob. 21ACh. 9.3A - Determine each of the following. a. What are the...Ch. 9.3A - Suppose five quarters, five dimes, fives nickels,...Ch. 9.3A - If the odds in favor of Fast Leg winning a horse...Ch. 9.3A - Prob. 25ACh. 9.3A - Carina is playing a game that costs 10 to play....Ch. 9.3A - Prob. 27ACh. 9.3A - Assessment If the probability of spilling soup on...Ch. 9.3A - Assessment A bag of grass seed is advertised as...Ch. 9.3A - Suppose you invented a game based on taking the...Ch. 9.3B - How could we use a spinner as shown below to...Ch. 9.3B - How could we use a random-digit generator or...Ch. 9.3B - Prob. 3ACh. 9.3B - Prob. 4ACh. 9.3B - Prob. 5ACh. 9.3B - Use a random-number table to estimate the...Ch. 9.3B - Prob. 10ACh. 9.3B - Prob. 11ACh. 9.3B - Prob. 12ACh. 9.3B - Prob. 13ACh. 9.3B - Prob. 14ACh. 9.3B - Two dice are rolled; find the odds against rolling...Ch. 9.3B - a. What are the odds in favor of randomly drawing...Ch. 9.3B - The probability that a person passes a test is 75....Ch. 9.3B - Prob. 18ACh. 9.3B - Prob. 19ACh. 9.3B - Determine each of the following. a. What are the...Ch. 9.3B - Prob. 21ACh. 9.3B - On a roulette wheel, half of the slots numbered 1...Ch. 9.3B - Suppose someone was playing the following dice...Ch. 9.3B - Suppose a standard six-sided die is rolled and you...Ch. 9.3B - Prob. 26ACh. 9.3B - Prob. 27ACh. 9.3B - Prob. 28ACh. 9.3B - Prob. 29ACh. 9.3B - Dean is playing a game that costs 10 to play. He...Ch. 9.4 - The terms Fundamental Counting Principle,...Ch. 9.4 - A bicycle lock has three reels, each of which...Ch. 9.4 - In how many ways can five couples be seated in a...Ch. 9.4 - Prob. 5MCCh. 9.4 - Prob. 6MCCh. 9.4 - Prob. 7MCCh. 9.4 - Prob. 8MCCh. 9.4 - Combination locks are poorly named, mainly because...Ch. 9.4 - A student does not understand the meaning of 4P0 ....Ch. 9.4 - Prob. 11MCCh. 9.4 - Prob. 12MCCh. 9.4 - Prob. 13MCCh. 9.4 - If two regular dice are tossed, what is...Ch. 9.4 - On a roulette wheel, the probability of the event...Ch. 9.4 - Prob. 1NAEPCh. 9.4 - Prob. 2NAEPCh. 9.4A - Prob. 1ACh. 9.4A - Prob. 2ACh. 9.4A - The eighth grade class at a grade school has 16...Ch. 9.4A - Prob. 4ACh. 9.4A - Carlins Pizza House offer 3 kinds of salad, 15...Ch. 9.4A - Prob. 6ACh. 9.4A - Find the number of ways to arrange the letter in...Ch. 9.4A - Prob. 8ACh. 9.4A - Assume a class has 30 members a. In how many ways...Ch. 9.4A - Prob. 10ACh. 9.4A - At a party, 28 handshakes took place. Each person...Ch. 9.4A - Prob. 12ACh. 9.4A - Postal codes in Canada consist of three letters...Ch. 9.4A - Baskin-Robbins advertises 31 flavors of ice cream....Ch. 9.4A - Prob. 15ACh. 9.4A - Prob. 16ACh. 9.4A - Prob. 17ACh. 9.4A - A five-volume numbered set of books is placed...Ch. 9.4A - Prob. 19ACh. 9.4A - Prob. 20ACh. 9.4A - From a group of 10 boys and 12 girls, a committee...Ch. 9.4A - From a group 20 Britons, 21 Italians, and 4 Danes,...Ch. 9.4A - Prob. 23ACh. 9.4A - A company is setting up four-digit ID numbers for...Ch. 9.4A - Your English teacher asks that you read any three...Ch. 9.4A - Prob. 26ACh. 9.4B - Prob. 1ACh. 9.4B - Prob. 2ACh. 9.4B - Assessment Radio stations in the United States...Ch. 9.4B - Prob. 5ACh. 9.4B - Find the number of ways to arrange the letters in...Ch. 9.4B - Prob. 7ACh. 9.4B - Prob. 8ACh. 9.4B - Prob. 10ACh. 9.4B - How many different 12-person juries can be...Ch. 9.4B - Prob. 12ACh. 9.4B - A club selects an executive committee of 5 and...Ch. 9.4B - Prob. 18ACh. 9.4B - A committee of three people is selected at random...Ch. 9.4B - Prob. 20ACh. 9.4B - Prob. 21ACh. 9.4B - Jackson has 20 books, but has space for only 12 on...Ch. 9.4B - Prob. 23ACh. 9.4B - In how many ways can a group of 9 people stand in...Ch. 9.4B - How many arrangements can be made from the letters...Ch. 9.CR - Prob. 1CRCh. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Art works as a clown on weekends. He has three...Ch. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - Prob. 10CRCh. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - A game consists of rolling two dice. Rolling...Ch. 9.CR - Prob. 15CRCh. 9.CR - In a special raffle, a ticket costs 2. You mark...Ch. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - Prob. 24CRCh. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 28CRCh. 9.CR - Suppose you spin a spinner and then roll a die....Ch. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Prob. 34CRCh. 9.CR - Prob. 35CRCh. 9.CR - Prob. 36CRCh. 9.CR - Prob. 37CRCh. 9.CR - Prob. 38CRCh. 9.CR - Prob. 39CRCh. 9 - Now Try This Use StatCrunch or another coin...Ch. 9 - NOW TRY THIS a. In an experiment of tossing a fair...Ch. 9 - Prob. 4NTCh. 9 - Prob. 6NTCh. 9 - Prob. 7NTCh. 9 - Prob. 8NTCh. 9 - Prob. 9NT
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