Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
12th Edition
ISBN: 9780137442966
Author: Larry Goldstein, David Schneider
Publisher: PEARSON+
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Chapter 4.4, Problem 15E
To determine
The matrix formulation of the linear programming problem,
Maximize
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7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies
the inequality
|P(z)| R.
Suggestion: Observe that there is a positive number R such that the modulus of
each quotient in inequality (9), Sec. 5, is less than |an|/n when |z| > R.
9. Establish the identity
1-
1+z+z² +
2n+1
...
+z" =
1- z
(z1)
and then use it to derive Lagrange's trigonometric identity:
1
1+ cos cos 20 +... + cos no =
+
2
sin[(2n+1)0/2]
2 sin(0/2)
(0 < 0 < 2л).
Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider
the difference S - zS. To derive the second identity, write z =
eie in the first one.
8. Prove that two nonzero complex numbers z₁ and Z2 have the same moduli if and only if
there are complex numbers c₁ and c₂ such that Z₁ = c₁C2 and Z2 = c1c2.
Suggestion: Note that
(i≤
exp (101+0) exp (01-02)
and [see Exercise 2(b)]
2
02
Ꮎ
-
= = exp(i01)
exp(101+0) exp (i 01 - 02 ) = exp(102).
i
2
2
Chapter 4 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYUCh. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...
Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...Ch. 4.1 - 7–12 For each of the linear programming problems...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - In Exercises 13–20, find the particular solution...Ch. 4.1 - In Exercises 1320, find the particular solution...Ch. 4.1 - In Exercises 13–20, find the particular solution...Ch. 4.1 - In Exercises 1320, find the particular solution...Ch. 4.1 - In Exercises 13–20, find the particular solution...Ch. 4.1 - Prob. 18ECh. 4.1 - In Exercises 13–20, find the particular solution...Ch. 4.1 - In Exercises 1320, find the particular solution...Ch. 4.1 - Pivot the simplex tableau...Ch. 4.1 - Pivot the simplex tableau...Ch. 4.1 - 23. (a) Name the group I and group II variables in...Ch. 4.1 - 24. (a) Name the group I and group II variables in...Ch. 4.2 - 1. Which of these simplex tableaux has a solution...Ch. 4.2 - Prob. 2CYUCh. 4.2 - In Exercises 1–6, determine the next pivot element...Ch. 4.2 - In Exercises 16, determine the next pivot element...Ch. 4.2 - In Exercises 16, determine the next pivot element...Ch. 4.2 - In Exercises 1–6, determine the next pivot element...Ch. 4.2 - Prob. 5ECh. 4.2 - In Exercises 16, determine the next pivot element...Ch. 4.2 - !! For each of the simplex tableaux in Exercises...Ch. 4.2 - For each of the simplex tableaux in Exercises...Ch. 4.2 - !! For each of the simplex tableaux in Exercises...Ch. 4.2 - For each of the simplex tableaux in Exercises...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - In Exercises 11–20, solve the linear programming...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - In Exercises 11–20, solve the linear programming...Ch. 4.2 - In Exercises 11–20, solve the linear programming...Ch. 4.2 - In Exercises 11–20, solve the linear programming...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - In Exercises 1120, solve the linear programming...Ch. 4.2 - 21. Toy Factory A toy manufacturer makes...Ch. 4.2 - 22. Agriculture A large agricultural firm has 250...Ch. 4.2 - 23. Furniture Factory Suppose that a furniture...Ch. 4.2 - Stereo Store A stereo store sells three brands of...Ch. 4.2 - Weight Loss and exercise As part of a...Ch. 4.2 - 26. Furniture Factory A furniture manufacturer...Ch. 4.2 - Prob. 27ECh. 4.2 - Baby Products A baby products company makes car...Ch. 4.2 - Potting Soil Mixes A lawn and garden store creates...Ch. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - 32. Maximize subject to the constraints
Ch. 4.2 - Maximize 60x+90y+300z subject to the constraints...Ch. 4.2 - 34. Maximize subject to the constraints
Ch. 4.2 - Maximize 2x+4y subject to the constraints...Ch. 4.2 - Prob. 36ECh. 4.2 - In Exercises 1–6, determine the next pivot element...Ch. 4.3 - 1. Convert the following minimum problem into a...Ch. 4.3 - Suppose that the solution of a minimum problem...Ch. 4.3 - In Exercises 14, write each linear programming...Ch. 4.3 - In Exercises 14, write each linear programming...Ch. 4.3 - In Exercises 1–4, write each linear programming...Ch. 4.3 - In Exercises 1–4, write each linear programming...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 916, solve the linear programming...Ch. 4.3 - In Exercises 9–16, solve the linear programming...Ch. 4.3 - In Exercises 9–16, solve the linear programming...Ch. 4.3 - In Exercises 9–16, solve the linear programming...Ch. 4.3 - Prob. 13ECh. 4.3 - In Exercises 916, solve the linear programming...Ch. 4.3 - In Exercises 916, solve the linear programming...Ch. 4.3 - Prob. 16ECh. 4.3 - 17. Nutrition A dietitian is designing a daily...Ch. 4.3 - Electronics Manufacture A manufacturing company...Ch. 4.3 - Supply and Demand An appliance store sells three...Ch. 4.3 - 20. Political Campaign A citizen decides to...Ch. 4.3 - Inventory A Manufacturer of computers must fill...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - 24. Maximize subject to the constraints
Ch. 4.4 - Consider the furniture manufacturing problem,...Ch. 4.4 - Prob. 2CYUCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Exercises 3 and 4 refer to the transportation...Ch. 4.4 - Exercises 3 and 4 refer to the transportation...Ch. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - In Exercises 13 and 14, give the matrix...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - 19. Create a sensitivity report for the...Ch. 4.4 - Create a sensitivity report for the nutrition...Ch. 4.5 - A linear programming problem involving three...Ch. 4.5 - Prob. 2CYUCh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - In Exercises 16, determine the dual problem of the...Ch. 4.5 - In Exercises 16, determine the dual problem of the...Ch. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - 7. The final simplex tableau for the linear...Ch. 4.5 - The final simplex tableau for the dual of the...Ch. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - In Exercises 11–14, determine the dual problem....Ch. 4.5 - Prob. 13ECh. 4.5 - In Exercises 11–14, determine the dual problem....Ch. 4.5 - 15. Cutting edge Knife Co. Give an economic...Ch. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Use the dual to solve Exercises 20 and 21....Ch. 4.5 - Use the dual to solve Exercises 20 and...Ch. 4 - 1. What is the standard maximization form of a...Ch. 4 - Prob. 2FCCECh. 4 - Prob. 3FCCECh. 4 - Give the steps for carrying out the simplex method...Ch. 4 - Prob. 5FCCECh. 4 - Prob. 6FCCECh. 4 - Prob. 7FCCECh. 4 - State the fundamental theorem of duality.Ch. 4 - Prob. 9FCCECh. 4 - 10. What is meant by “sensitivity analysis”?
Ch. 4 - Prob. 11FCCECh. 4 - In Exercises 1–10, use the simplex method to solve...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Determine the dual problem of the linear...Ch. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Consider the linear programming problems in...Ch. 4 - Prob. 17RECh. 4 - Nutrition A camp counselor wants to make a...Ch. 4 - Prob. 19RECh. 4 - 20. Stereo Store Consider the stereo store of...Ch. 4 - Jason’s House of Cheese offers two cheese...Ch. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Jasons House of Cheese offers two cheese...Ch. 4 - Jasons House of Cheese offers two cheese...Ch. 4 - Prob. 6P
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