Basic College Mathematics (12th Edition)
12th Edition
ISBN: 9780321931900
Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson
Publisher: PEARSON
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Chapter 5.4, Problem 46E
To determine
To find: The amount should be increased for Tim if he earning $23,000.
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Students have asked these similar questions
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
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).
Chapter 5 Solutions
Basic College Mathematics (12th Edition)
Ch. 5.1 - Prob. 1SRCh. 5.1 - Prob. 2SRCh. 5.1 - Prob. 1DECh. 5.1 - Find the ratio of 57.3 to 86.1.Ch. 5.1 - Prob. 3DECh. 5.1 - Record Snowfall. The greatest snowfall recorded in...Ch. 5.1 - Prob. 5DECh. 5.1 - Prob. 6DECh. 5.1 - Prob. 7DECh. 5.1 - Prob. 8DE
Ch. 5.1 - Prob. 9DECh. 5.1 - Prob. 10DECh. 5.1 - Prob. 11DECh. 5.1 - Prob. 1RCCh. 5.1 - Prob. 2RCCh. 5.1 - Prob. 3RCCh. 5.1 - Prob. 4RCCh. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 8ECh. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - a. Find fraction notation for each ratio. You need...Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - b. Find the ratio of the first number to the...Ch. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - For this right triangle, find the ratios of...Ch. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Find the ratio of 334 to 578 and simplify.Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.2 - Prob. 1SRCh. 5.2 - Divide using decimal notation. [4.4a] Divide. 2....Ch. 5.2 - Prob. 1DECh. 5.2 - Prob. 2DECh. 5.2 - Prob. 3DECh. 5.2 - Prob. 4DECh. 5.2 - Prob. 5DECh. 5.2 - Unit Price of Pasta Sauce. Gregory bought a 26-oz...Ch. 5.2 - Prob. 7DECh. 5.2 - Prob. 1RCCh. 5.2 - Prob. 2RCCh. 5.2 - Prob. 3RCCh. 5.2 - Complete each sentence with the correct quantity...Ch. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Broadway Musicals. In the 17 years from 1987...Ch. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Divide. Simplify, if possible. 42. 95 10 [4.4a]Ch. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.3 - Prob. 1SRCh. 5.3 - Prob. 2SRCh. 5.3 - Prob. 1DECh. 5.3 - Prob. 2DECh. 5.3 - Prob. 3DECh. 5.3 - Prob. 4DECh. 5.3 - Prob. 5DECh. 5.3 - Prob. 6DECh. 5.3 - Prob. 7DECh. 5.3 - Prob. 8DECh. 5.3 - Prob. 9DECh. 5.3 - Prob. 10DECh. 5.3 - Prob. 11DECh. 5.3 - Prob. 12DECh. 5.3 - Prob. 1RCCh. 5.3 - Prob. 2RCCh. 5.3 - Prob. 3RCCh. 5.3 - Prob. 4RCCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - a Determine whether the two pairs of numbers are...Ch. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - b Solve. 22. 89=32nCh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - b Solve. 39. 82.4=6yCh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.4 - Prob. 1SRCh. 5.4 - Solve equations of the type a x = b, where a and...Ch. 5.4 - Prob. 1DECh. 5.4 - Prob. 2DECh. 5.4 - Prob. 3DECh. 5.4 - Prob. 4DECh. 5.4 - Prob. 5DECh. 5.4 - Prob. 6DECh. 5.4 - Prob. 1RCCh. 5.4 - Prob. 2RCCh. 5.4 - Prob. 3RCCh. 5.4 - Prob. 4RCCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Painting. Fred uses 3 gal of paint to cover 1275...Ch. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Estimating a Whak Population. To determine the...Ch. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - 42. 0.078 = 0.3·t [4.4b]
Ch. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Carney College is expanding from 850 to 1050...Ch. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.5 - Prob. 1SRCh. 5.5 - Prob. 2SRCh. 5.5 - Prob. 1DECh. 5.5 - Prob. 2DECh. 5.5 - Prob. 3DECh. 5.5 - Prob. 4DECh. 5.5 - Prob. 5DECh. 5.5 - Prob. 6DECh. 5.5 - Prob. 1RCCh. 5.5 - Prob. 2RCCh. 5.5 - Prob. 3RCCh. 5.5 - Prob. 4RCCh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - How high is a tree that casts a 27-ft shadow at...Ch. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - bIn each of Exercises 17-26. the sides in each...Ch. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Prob. 44ECh. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5 - Determine whether each statement is true or false....Ch. 5 - Prob. 2MCCh. 5 - Prob. 3MCCh. 5 - Prob. 4MCCh. 5 - Prob. 5MCCh. 5 - Prob. 6MCCh. 5 - Prob. 7MCCh. 5 - Prob. 8MCCh. 5 - Prob. 9MCCh. 5 - Prob. 10MCCh. 5 - Prob. 11MCCh. 5 - Prob. 12MCCh. 5 - Prob. 13MCCh. 5 - Prob. 14MCCh. 5 - Prob. 15MCCh. 5 - Prob. 16MCCh. 5 - Prob. 17MCCh. 5 - Prob. 18MCCh. 5 - Prob. 19MCCh. 5 - Prob. 20MCCh. 5 - Prob. 21MCCh. 5 - Prob. 22MCCh. 5 - Prob. 23MCCh. 5 - Prob. 24MCCh. 5 - Prob. 25MCCh. 5 - Prob. 26MCCh. 5 - Prob. 27MCCh. 5 - Prob. 28MCCh. 5 - Prob. 29MCCh. 5 - Prob. 30MCCh. 5 - Prob. 31MCCh. 5 - Prob. 32MCCh. 5 - Prob. 33MCCh. 5 - Prob. 34MCCh. 5 - Prob. 35MCCh. 5 - Prob. 36MCCh. 5 - Prob. 37MCCh. 5 - Prob. 38MCCh. 5 - Prob. 1VRCh. 5 - Prob. 2VRCh. 5 - Prob. 3VRCh. 5 - Prob. 4VRCh. 5 - Prob. 5VRCh. 5 - Prob. 6VRCh. 5 - Prob. 1CRCh. 5 - Prob. 2CRCh. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - Prob. 1PECh. 5 - Prob. 2PECh. 5 - Prob. 3PECh. 5 - Prob. 4PECh. 5 - Prob. 5PECh. 5 - Prob. 6PECh. 5 - Prob. 7PECh. 5 - Prob. 8PECh. 5 - Prob. 1RECh. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Find the ratio of the first number to the second...Ch. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Solve. [5.3b] 17. 6x=4856Ch. 5 - Prob. 18RECh. 5 - Solve. [5.3b] 19. 4.5120=0.9xCh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - How high is a billboard that casts a 25-ft shadow...Ch. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Write fraction notation for each ratio. Do not...Ch. 5 - Prob. 3TCh. 5 - Prob. 4TCh. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Prob. 7TCh. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Determine whether the two pairs of numbers are...Ch. 5 - Prob. 12TCh. 5 - Prob. 13TCh. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 16TCh. 5 - Prob. 17TCh. 5 - Prob. 18TCh. 5 - Prob. 19TCh. 5 - Charity Work. Kayla is crocheting hats for a...Ch. 5 - Prob. 21TCh. 5 - Prob. 22TCh. 5 - Prob. 23TCh. 5 - Prob. 24TCh. 5 - Prob. 25TCh. 5 - Prob. 1CURCh. 5 - Prob. 2CURCh. 5 - Prob. 3CURCh. 5 - Prob. 4CURCh. 5 - Prob. 5CURCh. 5 - Prob. 6CURCh. 5 - Prob. 7CURCh. 5 - Prob. 8CURCh. 5 - Prob. 9CURCh. 5 - Prob. 10CURCh. 5 - Prob. 11CURCh. 5 - Prob. 12CURCh. 5 - Prob. 13CURCh. 5 - Prob. 14CURCh. 5 - Prob. 15CURCh. 5 - Prob. 16CURCh. 5 - Prob. 17CURCh. 5 - Prob. 18CURCh. 5 - Prob. 19CURCh. 5 - Prob. 20CURCh. 5 - Prob. 21CURCh. 5 - Prob. 22CURCh. 5 - Prob. 23CURCh. 5 - Prob. 24CURCh. 5 - Prob. 25CURCh. 5 - Prob. 26CURCh. 5 - Prob. 27CURCh. 5 - Prob. 28CURCh. 5 - Prob. 29CURCh. 5 - Prob. 30CURCh. 5 - Prob. 31CURCh. 5 - Prob. 32CURCh. 5 - Prob. 33CURCh. 5 - Prob. 34CURCh. 5 - Prob. 35CURCh. 5 - Prob. 36CURCh. 5 - Prob. 37CURCh. 5 - Prob. 38CURCh. 5 - Prob. 39CURCh. 5 - Prob. 40CURCh. 5 - Prob. 41CUR
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