Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
11th Edition
ISBN: 9780134434636
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 9.1, Problem 20E
To determine
The vector sum
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Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction
of the objective function. Use you sketch to find an optimal solution to the
program. State the optimal solution and give the objective value for this
solution.
maximize +22
subject to 1 + 2x2 ≤ 4,
1 +3x2 ≤ 12,
x1, x2 ≥0
(b) For the following linear programme, sketch the feasible region and the direction
of the objective function. Explain, making reference to your sketch, why this
linear programme is unbounded.
maximize
₁+%2
subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
x1,x20
Give any feasible solution to the linear programme for which the objective
value is 40 (you do not need to justify your answer).
find the domain of the function f(x)
Chapter 9 Solutions
Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PECh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8E
Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - In Exercises 15–18, draw the given vectors and...Ch. 9.1 - Prob. 17ECh. 9.1 - In Exercises 15–18, draw the given vectors and...Ch. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - In Exercises 19–40, find the indicated vector sums...Ch. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - In Exercises 19–40, find the indicated vector sums...Ch. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - In Exercises 41–48, solve the given problems. Use...Ch. 9.1 - Prob. 48ECh. 9.2 - For the vector in Example 1, change the angle to...Ch. 9.2 - Prob. 2PECh. 9.2 - Prob. 3PECh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - In Exercises 5–10, find the horizontal and...Ch. 9.2 - Prob. 7ECh. 9.2 - In Exercises 5–10, find the horizontal and...Ch. 9.2 - Prob. 9ECh. 9.2 - In Exercises 5–10, find the horizontal and...Ch. 9.2 - Prob. 11ECh. 9.2 - In Exercises 11–20, find the x- and y-components...Ch. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - In Exercises 11–20, find the x- and y-components...Ch. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - In Exercises 11–20, find the x- and y-components...Ch. 9.2 - In Exercises 21–34, find the required horizontal...Ch. 9.2 - In Exercises 21–34, find the required horizontal...Ch. 9.2 - Prob. 23ECh. 9.2 - In Exercises 21–34, find the required horizontal...Ch. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - In Exercises 21–34, find the required horizontal...Ch. 9.2 - Prob. 29ECh. 9.2 - In Exercises 21–34, find the required horizontal...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.3 - Prob. 1PECh. 9.3 - Prob. 2PECh. 9.3 - Prob. 3PECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - In Exercises 3–6, vectors A and B are at right...Ch. 9.3 - In Exercises 3–6, vectors A and B are at right...Ch. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - In Exercises 7–14, with the given sets of...Ch. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - Prob. 28ECh. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - In order to move an ocean liner into the channel,...Ch. 9.3 - In Exercises 15–32, add the given vectors by...Ch. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.4 - A ship sails 32.50 mi due east and then turns...Ch. 9.4 - Prob. 2PECh. 9.4 - EXAMPLE 5 Equilibrium—forces on a climber
A 165-lb...Ch. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - A jet is 115 mi east and 88.3 mi north of Niagara...Ch. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Toronto is 650 km at 19.0° north of east from...Ch. 9.4 - Prob. 9ECh. 9.4 - A rocket is launched with a vertical component of...Ch. 9.4 - In testing the behavior of a tire on ice, a force...Ch. 9.4 - To raise a crate, two ropes are attached to its...Ch. 9.4 - A storm front is moving east at 18.0 km/h and...Ch. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - In an automobile safety test, a shoulder and seat...Ch. 9.4 - Prob. 18ECh. 9.4 - A plane flies at 550 km/h into a head wind of 60...Ch. 9.4 - A ship’s navigator determines that the ship is...Ch. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - On a mountain trek, a pack mule becomes obstinate...Ch. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - A mine shaft goes due west 75 m from the opening...Ch. 9.4 - Prob. 29ECh. 9.4 -
A scuba diver’s body is directed downstream at...Ch. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - A plane is moving at 75.0 m/s, and a package with...Ch. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.5 - Prob. 1PECh. 9.5 - Prob. 2PECh. 9.5 - Prob. 3PECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - In Exercises 3–20, solve the triangles with the...Ch. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - A small island is approximately a triangle in...Ch. 9.5 - A boat followed a triangular route going from dock...Ch. 9.5 - The loading ramp at a delivery service is 12.5 ft...Ch. 9.5 - In an aerial photo of a triangular field, the...Ch. 9.5 - The Pentagon (headquarters of the U.S. Department...Ch. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - When an airplane is landing at an 8250-ft runway,...Ch. 9.5 - Find the total length of the path of the laser...Ch. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.6 - Prob. 1PECh. 9.6 - Prob. 2PECh. 9.6 - Prob. 1ECh. 9.6 - Prob. 2ECh. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - Prob. 6ECh. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - In Exercises 3–20, solve the triangles with the...Ch. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Prob. 29ECh. 9.6 - In Exercises 21–40, use the law of cosines to...Ch. 9.6 - Prob. 31ECh. 9.6 - Prob. 32ECh. 9.6 - In Exercises 21–40, use the law of cosines to...Ch. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - In Exercises 21–40, use the law of cosines to...Ch. 9.6 - Prob. 38ECh. 9.6 - Prob. 39ECh. 9.6 - Prob. 40ECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - In Exercises 15–22, add the given vectors by using...Ch. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - In Exercises 41–74, solve the given problems.
42....Ch. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - In Exercises 41–74, solve the given...Ch. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - Prob. 75RECh. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Prob. 6PTCh. 9 - Prob. 7PTCh. 9 - Prob. 8PTCh. 9 - Prob. 9PTCh. 9 - Prob. 10PTCh. 9 - Prob. 11PT
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