Contemporary Mathematics for Business and Consumers
7th Edition
ISBN: 9781285189758
Author: Robert Brechner, George Bergeman
Publisher: Cengage Learning
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Chapter 15.I, Problem 3TIE
To determine
The complete balance sheet of provided comparative balance sheet of Calypso Industries, Inc. for December
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Suppose we have a linear program in standard equation form
maximize cTx
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) 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
x2 x3
81 82
83
84
81
-2 0
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
Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
Chapter 15 Solutions
Contemporary Mathematics for Business and Consumers
Ch. 15.I - Use the following financial information to prepare...Ch. 15.I - Prob. 2TIECh. 15.I - Prob. 3TIECh. 15.I - Prob. 1RECh. 15.I - Prob. 2RECh. 15.I - Prob. 3RECh. 15.I - Prob. 4RECh. 15.I - Prob. 5RECh. 15.I - Prob. 6RECh. 15.I - Calculate the following values according to the...
Ch. 15.I - Prob. 8RECh. 15.I - Calculate the missing balance sheet items for...Ch. 15.I - Prob. 10RECh. 15.I - Prob. 11RECh. 15.I - Prob. 12RECh. 15.I - Prob. 13RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 16RECh. 15.I - Prob. 17RECh. 15.I - Prob. 18RECh. 15.I - Prob. 19RECh. 15.I - Prob. 20RECh. 15.I - Prob. 21RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 23RECh. 15.I - Prob. 24RECh. 15.I - Prob. 25RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 27RECh. 15.I - Prob. 28RECh. 15.I - Prob. 29RECh. 15.I - Prob. 30RECh. 15.I - Prob. 31RECh. 15.I - Prob. 32RECh. 15.I - Prob. 33RECh. 15.I - Prepare the following statements on separate...Ch. 15.I - a. Use the following financial information to...Ch. 15.II - Prob. 4TIECh. 15.II - Prob. 5TIECh. 15.II - Prob. 6TIECh. 15.II - Prob. 1RECh. 15.II - Prob. 2RECh. 15.II - Prob. 3RECh. 15.II - Prob. 4RECh. 15.II - Calculate the missing information based on the...Ch. 15.II - Prob. 6RECh. 15.II - Prob. 7RECh. 15.II - Prob. 8RECh. 15.II - Prob. 9RECh. 15.II - Prob. 10RECh. 15.II - Prob. 11RECh. 15.II - 12. For the third quarter. Micro Tech had gross...Ch. 15.II - For August, Island Traders, Inc. had the following...Ch. 15.II - Prepare the following statements on separate...Ch. 15.II - Prepare the following statements on separate...Ch. 15.III - Use the balance sheet and income statement on...Ch. 15.III - Prob. 8TIECh. 15.III - Prob. 1RECh. 15.III - Prob. 2RECh. 15.III - Prob. 3RECh. 15.III - Prob. 4RECh. 15.III - Prob. 5RECh. 15.III - Prob. 6RECh. 15.III - Prob. 7RECh. 15.III - Prob. 8RECh. 15.III - Prob. 9RECh. 15.III - Prob. 10RECh. 15.III - Prob. 11RECh. 15.III - Prob. 12RECh. 15.III - Prob. 13RECh. 15.III - Prob. 14RECh. 15.III - Calculate the average inventory and inventory...Ch. 15.III - Prob. 16RECh. 15.III - Prob. 17RECh. 15.III - Prob. 18RECh. 15.III - Prob. 19RECh. 15.III - Prob. 20RECh. 15.III - Prob. 21RECh. 15.III - Prob. 22RECh. 15.III - Prob. 23RECh. 15.III - Prob. 24RECh. 15.III - Calculate the gross and net profits and the two...Ch. 15.III - Prob. 26RECh. 15.III - Prob. 27RECh. 15.III - Prob. 28RECh. 15.III - Prob. 29RECh. 15.III - Prob. 30RECh. 15.III - Prob. 31RECh. 15.III - Prob. 32RECh. 15.III - Prob. 33RECh. 15 - 1. In accounting, economic resources owned by a...Ch. 15 - 2. The financial statement that illustrates the...Ch. 15 - 3. The balance sheet is a visual presentation of...Ch. 15 - Prob. 4CRCh. 15 - 5. A financial statement prepared with the data...Ch. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 1ATCh. 15 - Prob. 2ATCh. 15 - Prob. 3ATCh. 15 - Prob. 4ATCh. 15 - a. Use the following financial information to...Ch. 15 - a. Use the following financial information to...Ch. 15 - For the second quarter. Evergreen Plant Nursery...Ch. 15 - 8. For the month of January. Consolidated Engine...Ch. 15 - Prob. 9ATCh. 15 - a. Use the following financial information to...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - Prob. 22ATCh. 15 - Prob. 23ATCh. 15 - 24. From the following consolidated statements of...
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