Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 10.3, Problem 43E
Exercises 37-44 can be solved using combinations even though the problem statements will not always include the word "combination" or "subset."
Number of Paths from Point to Point In a certain city, there are seven streets going north-south and four streets going east-west. How many street paths start at the southwest corner of the city, end at the northeast corner of the city, and have the shortest possible length? (Mathematics Teacher calendar problem)
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Problem 3. Pricing a multi-stock option the Margrabe formula
The purpose of this problem is to price a swap option in a 2-stock model, similarly as
what we did in the example in the lectures. We consider a two-dimensional Brownian
motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices
are modeled by the following equations:
dX
=
dY₁ =
X₁ (rdt+
rdt+0₁dW!)
(²)),
Y₁ (rdt+dW+0zdW!"),
with Xo
xo and Yo =yo. This corresponds to the multi-stock model studied in class,
but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure
P is already the risk-neutral measure (Both stocks have rate of return r). We write
σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to
exchange one share of X for one share of Y. That is, the option has payoff
F=(Yr-XT).
(a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for
the process Xt.
Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
(b) Using the formulas obtained in (a), show that the process (WA) is actually a 2-
dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
Roedel Electronics produces tablet computer accessories, including integrated keyboard tablet stands that connect a keyboard to a tablet device and holds the device at a preferred angle for easy viewing and typing. Roedel produces two sizes of integrated keyboard tablet stands, small and large. Each size uses the same keyboard attachment,
but the stand consists of two different pieces, a top flap and a vertical stand that differ by size. Thus, a completed integrated keyboard tablet stand consists of three subassemblies that are manufactured by Roedel: a keyboard, a top flap, and a vertical stand.
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Chapter 10 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...
Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Construct a product table showing all possible...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - 49. Find the number of paths from A to B in the...Ch. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Work each problem.
52. Shaking Hands in a Group A...Ch. 10.1 - Work each problem. Number of Games in a Chess...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Work each problem. Selecting Dinner Items Michael...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Work each problem. Building Numbers from Sets of...Ch. 10.1 - Work each problem. Lattice Points on a Line...Ch. 10.1 - Work each problem.
64. Lengths of Segments Joining...Ch. 10.1 - Work each problem. Patterns in Floor Tiling A...Ch. 10.1 - Work each problem, Counting Matchsticks in a Grid...Ch. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 9ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - Use a calculator to evaluate each expression. 10!Ch. 10.2 - Use a calculator to evaluate each expression.
18....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
23....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
26. ...Ch. 10.2 - Use a calculator to evaluate each expression.
27. ...Ch. 10.2 - Use a calculator to evaluate each expression.
28. ...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 34ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 36ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Matching Club Members with Tasks Recall the club...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 54ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - 62. Listing Phone Numbers Raj keeps the phone...Ch. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 67ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 69ECh. 10.2 - Work each problem. Palindromes How many of the...Ch. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.3 - Evaluate each expression. 9P3Ch. 10.3 - Evaluate each expression.
2.
Ch. 10.3 - Evaluate each expression.
3.
Ch. 10.3 - Evaluate each expression. 11P3Ch. 10.3 - Evaluate each expression.
5.
Ch. 10.3 - Evaluate each expression.
6.
Ch. 10.3 - Evaluate each expression. 10C8Ch. 10.3 - Evaluate each expression.
8.
Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Use a calculator to evaluate each expression. 22P9Ch. 10.3 - Use a calculator to evaluate each expression....Ch. 10.3 - Use a calculator to evaluate each expression.
19....Ch. 10.3 - Use a calculator to evaluate each expression.
20....Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Prob. 25ECh. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Prob. 36ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 4ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 8ECh. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Prob. 12ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 14ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 16ECh. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Prob. 20ECh. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - How many subsets (of any size) are there for a set...Ch. 10.4 - 28. For a given row in Pascal's triangle, let n be...Ch. 10.4 - 29. Which rows of Pascal's triangle have a single...Ch. 10.4 - 30. What is the least four-digit number in...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Tartaglia's Rectangle More than a century before...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.5 - How many proper subsets are there of each set?
1....Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Identifying Properties of Counting Numbers Flow...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Choosing Country Music Albums Jeanne's collection...Ch. 10.5 - Choosing Broadway Hits The ten longest Broadway...Ch. 10.5 - 23. Choosing Days of the Week How many different...Ch. 10.5 - Choosing School Assignments tor Completion Diona...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Seating Arrangements on an Airliner Refer to...Ch. 10.5 - 28. Identifying Properties of Counting Numbers...Ch. 10.5 - 29. Counting Radio Call Letters Radio stations in...Ch. 10.5 - 30. Selecting Faculty Committees A committee of...Ch. 10.5 - Selecting Search-and-Rescue Teams A Civil Air...Ch. 10.5 - Choosing Team Members Three students from a class...Ch. 10.5 - Prob. 33ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Prob. 35ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Prob. 39ECh. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Prob. 45ECh. 10.5 - Counting Card Hands Among the 2,598,960possible...Ch. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Triangles in a Figure Determine the...Ch. 10 - Tossing Coins Construct a tree diagram showing all...Ch. 10 - 7. Sums of Digits How many nonrepeating four-digit...Ch. 10 - 8. Arranging Children Yeo has invited her sister...Ch. 10 - Evaluate each expression. 6!Ch. 10 - Evaluate each expression. 8!6!Ch. 10 - Evaluate each expression.
11.
Ch. 10 - Evaluate each expression.
12.
Ch. 10 - Building Words from Sets of Letters How many...Ch. 10 - Building Words from Sets of Letters Using the...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball PlayersIf there are...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Prob. 23TCh. 10 - Prob. 24TCh. 10 - Prob. 25TCh. 10 - Prob. 26TCh. 10 - Prob. 27TCh. 10 - Prob. 28TCh. 10 - Prob. 29TCh. 10 - Prob. 30TCh. 10 - Prob. 31TCh. 10 - Prob. 32TCh. 10 - Prob. 33TCh. 10 - Prob. 34TCh. 10 - Prob. 35TCh. 10 - Prob. 36T
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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…arrow_forwardConsider 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…arrow_forwardConsider 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).arrow_forward
- Statement:If 2 | a and 3| a, then 6 a. So find three integers, and at least one integer should be negative. For each of your examples, determine if the statement is true or false.arrow_forwardStatement: If 4 | a and 6 | a, then 24 | a. So find three integers, and at least one integer should be negative. For each of your examples, determine if the statement is true or false.arrow_forward2) dassify each critical point of the given plane autovers system x'=x-2x²-2xy y' = 4y-Sy³-7xyarrow_forward
- Evaluate the next integralarrow_forward1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4arrow_forward24.2. Show that, for any constant zo Є C, (a). e* = e²o Σ j=0 (2 - 20); j! |z|arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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