Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137553341
Author: Raymond Barnett, Michael Ziegler
Publisher: PEARSON+
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Chapter 6.1, Problem 68E
To determine
To explain: The reason behind the linear programming problem has no optimal solution.
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(^)
k
Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as
n!
k! (n−k)!
Question 1.
(1) Prove the following identity: (22) + (1121) = (n+1).
(2) Use the identity above to prove the binomial theorem by induction. That
is, prove that for any a, b = R,
n
(a + b)" = Σ (^)
an-
n-kyk.
k=0
n
Recall that Σ0 x is short hand notation for the expression x0+x1+
+xn-
(3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using
the binomial theorem.
-
Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y.
Question 3. Assume (In) nEN is a sequence which is unbounded above. That is,
the set {xn|nЄN} is unbounded above. Prove that there are natural numbers
N] k for all k Є N.
be natural numbers (nk Є N). Prove that
Question content area top
Part 1
Find the measure of
ABC
for the congruent triangles ABC and
Upper A prime Upper B prime Upper C primeA′B′C′.
79 degrees79°
1533
2930
Part 1
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ABCequals=enter your response heredegrees
Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways 
Chapter 6 Solutions
Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
Ch. 6.1 - Refer to Example 1. Find the basic solution for...Ch. 6.1 - Construct the table of basic solutions and use it...Ch. 6.1 - Prob. 3MPCh. 6.1 - Prob. 4MPCh. 6.1 - Prob. 1EDCh. 6.1 - The following linear programming problem has only...Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4E
Ch. 6.1 - In how many ways can two variables be chosen from...Ch. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 -
Problems 9–12 refer to the system
9. Find the...Ch. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - In Problems 13–20, write the e-system obtained via...Ch. 6.1 - In Problems 13–20, write the e-system obtained via...Ch. 6.1 - In Problems 13–20, write the e-system obtained via...Ch. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Problems 31–40 refer to the partially completed...Ch. 6.1 - Prob. 40ECh. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - In Problems 41-48, convert the given i-system to...Ch. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - In Problems 59-66, solve the given linear...Ch. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - In Problems 67-70, explain why the linear...Ch. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.2 - Solve the following linear programming problem...Ch. 6.2 - Solve using the simplex method:
Ch. 6.2 - Prob. 3MPCh. 6.2 - Prob. 1EDCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - In Problems 9–12,
Using slack variables, write the...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Prob. 14ECh. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Repeat Problem 17 with P = x1 + 2x2.
17.
Ch. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Prob. 24ECh. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Solve the linear programming problems in Problems...Ch. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - In Problems 37–40, there is a tie for the choice...Ch. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.3 - Form the dual problem:
Ch. 6.3 - Prob. 2MPCh. 6.3 - Prob. 3MPCh. 6.3 - Repeat Example 4 if the shipping charge from plant...Ch. 6.3 - Prob. 1EDCh. 6.3 - Prob. 2EDCh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - In Problems 1–8, find the transpose of each...Ch. 6.3 - In Problems 9 and 10,
Form the dual problem.
Write...Ch. 6.3 - Prob. 10ECh. 6.3 - In Problems 11 and 12, a minimization problem, the...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - In Problems 13–20,
Form the dual problem.
Find the...Ch. 6.3 - In Problems 13–20,
Form the dual problem.
Find the...Ch. 6.3 - Prob. 16ECh. 6.3 - In Problems 13–20,
Form the dual problem.
Find the...Ch. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Solve the linear programming problems in Problems...Ch. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Solve the linear programming problems in Problems...Ch. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Prob. 49ECh. 6.3 - Mining. A mining company operates two mines, each...Ch. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.4 - Repeat Example 1 for
EXAMPLE 1
Finding the...Ch. 6.4 - Prob. 2MPCh. 6.4 - Prob. 3MPCh. 6.4 - Prob. 4MPCh. 6.4 - Prob. 5MPCh. 6.4 - Interpret the values of the slack and surplus...Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Use the big M method to solve Problems 9–22.
9.
Ch. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Use the big M method to solve Problems 9–22.
13.
Ch. 6.4 - Prob. 14ECh. 6.4 - Use the big M method to solve Problems 9–22.
15.
Ch. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Use the big M method to solve Problems 9-22.
21....Ch. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Problems 25–32 are mixed. Some can be solved by...Ch. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - In Problems 33–38, construct a mathematical model...Ch. 6.4 - In Problems 33–38, construct a mathematical model...Ch. 6.4 - In Problems 33-38, construct a mathematical model...Ch. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - In Problems 28 and 29,
Introduce slack, surplus,...Ch. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RE
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