Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134506470
Author: Pirnot
Publisher: PEARSON
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Chapter 12.3, Problem 29E
To determine
To describe:
The element
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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to
determine which cities Martin-Beck should construct a plant in.
Let
y₁ = 1 if a plant is constructed in Detroit; 0 if not
y₂ = 1 if a plant is constructed in Toledo; 0 if not
y₂ = 1 if a plant is constructed in Denver; 0 if not
y = 1 if a plant is constructed in Kansas City; 0 if not.
The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem.
*,, = the units shipped in thousands from plant i to distribution center j
i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and…
Consider the following mixed-integer linear program.
Max
3x1
+
4x2
s.t.
4x1
+
7x2
≤
28
8x1
+
5x2
≤
40
x1, x2 ≥ and x1 integer
(a)
Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several horizontal lines are on the graph.
The series of line segments connect the approximate points (0, 4), (3.889, 1.778), and (5, 0).
The region is above the horizontal axis, to the right of the vertical axis, and below the line segments.
At each integer value between 0 and 4 on the vertical axis, a horizontal line extends out from the vertical axis to the series of connect line segments.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several…
Consider the nonlinear optimization model stated below.
Min
s.t.
2x²-18x + 2XY + y² - 14Y + 53
x + 4Y ≤ 8
(a) Find the minimum solution to this problem.
|at (X, Y) =
(b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change?
Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by
(c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate?
If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is|
, so the actual change is a decrease of
rather than what we expected in part (b).
Chapter 12 Solutions
Mathematics All Around (6th Edition)
Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - How many different two-digit numbers can you form...Ch. 12.1 - How many different two-digit numbers can you form...
Ch. 12.1 - How many different three-digit numbers can you...Ch. 12.1 - How many different three-digit numbers can you...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - Recall in Example 6 that you are creating outfits...Ch. 12.1 - Recall in Example 6 that you are creating outfits...Ch. 12.1 - Use the given diagram to solve Exercises 21 and...Ch. 12.1 - Use the given diagram to solve Exercises 21 and...Ch. 12.1 - Answer Exercise 21 assuming the diagram has six...Ch. 12.1 - Prob. 24ECh. 12.1 - Assigning tasks. Stefans friends Amika, Pam, Li,...Ch. 12.1 - Making staff assignments. Suppose that the staff...Ch. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - The role-playing game Dungeons & Dragons uses a...Ch. 12.1 - Dungeons & Dragons also uses 12-sided dice. How...Ch. 12.1 - Counting license plates. An eyewitness to a crime...Ch. 12.1 - Counting license plates. In a small state, the...Ch. 12.1 - For Exercises 33 and 34, use the figures below....Ch. 12.1 - For Exercises 33 and 34, use the figures below....Ch. 12.1 - Prince William and Duchess Kate are attending the...Ch. 12.1 - Prince William and Duchess Kate are attending the...Ch. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Stacking cans. In preparation for Thanksgiving...Ch. 12.1 - Prob. 40ECh. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.2 - Assigning responsibilities. The board of an...Ch. 12.2 - Assigning positions. If there are 12 members on...Ch. 12.2 - Assigning officers. The Equestrian Club has eight...Ch. 12.2 - Assigning officers. If the Chamber of Commerce has...Ch. 12.2 - Choosing a stand up paddle board package. Kevin...Ch. 12.2 - Counting schedules. Jorge is using his educational...Ch. 12.2 - Counting meal possibilities. The early bird...Ch. 12.2 - Prob. 8ECh. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - Prob. 16ECh. 12.2 - A truefalse quiz. In how many ways can you choose...Ch. 12.2 - A multiple-choice test. In how many ways can you...Ch. 12.2 - Planning a trip. Center City Community Colleges...Ch. 12.2 - A piano competition. In the Van Cliburn piano...Ch. 12.2 - Enumerating call letters. Radio stations in the...Ch. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Counting license plates. In a certain state,...Ch. 12.2 - A pin tumbler lock has a series of pins, each of...Ch. 12.2 - A pin tumbler lock has a series of pins, each of...Ch. 12.2 - Counting routes for an armored van. A Wells Fargo...Ch. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Facial arrangements. A website enables you to...Ch. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Exercises 33 and 34 are alternative versions of...Ch. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - In solving counting problems, it is often useful...Ch. 12.2 - What is the relationship between trees, slot...Ch. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.3 - In Exercises 112, calculate each value. 4!Ch. 12.3 - Prob. 2ECh. 12.3 - In Exercises 112, calculate each value. (85)!Ch. 12.3 - In Exercises 112, calculate each value. (105)!Ch. 12.3 - In Exercises 112, calculate each value. 107Ch. 12.3 - In Exercises 112, calculate each value. 119Ch. 12.3 - Prob. 7ECh. 12.3 - In Exercises 112, calculate each value. 1192Ch. 12.3 - In Exercises 112, calculate each value. P(6,2)Ch. 12.3 - In Exercises 112, calculate each value. P(5,3)Ch. 12.3 - In Exercises 112, calculate each value. C(10,3)Ch. 12.3 - In Exercises 112, calculate each value. C(4,4)Ch. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1922, find the number of...Ch. 12.3 - Prob. 20ECh. 12.3 - In Exercises 1922, find the number of...Ch. 12.3 - Prob. 22ECh. 12.3 - Find the eighth row in Pascals triangle.Ch. 12.3 - Find the tenth row in Pascals triangle.Ch. 12.3 - Use the seventh row of Pascals triangle to answer...Ch. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - In Exercises 2730, describe where each number is...Ch. 12.3 - Prob. 29ECh. 12.3 - In Exercises 2730, describe where each number is...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 32ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 34ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 42ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 4548, determine the number of ways to...Ch. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - In Exercise 49 and 50, determine why the given...Ch. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - A typical bingo card is shown in the figure. The...Ch. 12.3 - Prob. 53ECh. 12.3 - A typical bingo card is shown in the figure. The...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 62ECh. 12.3 - Prob. 63ECh. 12.3 - Prob. 64ECh. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Prob. 73ECh. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Prob. 80ECh. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Prob. 85ECh. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.3 - Prob. 88ECh. 12.3 - Prob. 89ECh. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Prob. 5ECh. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Prob. 9ECh. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Prob. 13ECh. 12.4 - Why are we using combinations rather than...Ch. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Playing poker. How many poker hands are less in...Ch. 12.CR - Prob. 1CRCh. 12.CR - The game Dungeons & Dragons uses a tetrahedral die...Ch. 12.CR - Prob. 3CRCh. 12.CR - Prob. 4CRCh. 12.CR - Prob. 5CRCh. 12.CR - Prob. 6CRCh. 12.CR - Prob. 7CRCh. 12.CR - Prob. 8CRCh. 12.CR - Prob. 9CRCh. 12.CR - Prob. 10CRCh. 12.CR - You are going to serve gourmet cupcakes at your...Ch. 12.CR - Prob. 12CRCh. 12.CR - Prob. 13CRCh. 12.CR - Prob. 14CRCh. 12.CR - Prob. 15CRCh. 12.CR - Prob. 16CRCh. 12.CR - Prob. 17CRCh. 12.CT - List all the ways you can select two different...Ch. 12.CT - Prob. 2CTCh. 12.CT - Prob. 3CTCh. 12.CT - Use the sixth row of Pascals triangle to find the...Ch. 12.CT - Prob. 5CTCh. 12.CT - Prob. 6CTCh. 12.CT - Prob. 7CTCh. 12.CT - Prob. 8CTCh. 12.CT - Prob. 9CTCh. 12.CT - Prob. 10CTCh. 12.CT - Prob. 11CTCh. 12.CT - Prob. 12CTCh. 12.CT - Write an equation that relates the expressions...Ch. 12.CT - Prob. 14CTCh. 12.CT - Prob. 15CTCh. 12.CT - Prob. 16CT
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