Practical Business Math Procedures
12th Edition
ISBN: 9781259540554
Author: Jeffrey Slater, Sharon Wittry
Publisher: McGraw-Hill Education
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Chapter 3, Problem 9CR
To determine
The total cost on the second day from given data.
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Client
1
Weight before
diet (pounds)
Weight after
diet (pounds)
128
120
2
131
123
3
140
141
4
178
170
5
121
118
6
136
136
7
118
121
8
136
127
a) Determine the mean change in patient weight from before to after the
diet (after – before). What is the 95% confidence interval of this mean
difference?
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
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.
Chapter 3 Solutions
Practical Business Math Procedures
Ch. 3.1 - Write the following as a decimal number.
Four...Ch. 3.1 - Prob. 2PQCh. 3.1 - Prob. 3PQCh. 3.1 - Prob. 4PQCh. 3.1 - Prob. 5PQCh. 3.1 - Prob. 6PQCh. 3.1 - Convert the following to decimals:
Ch. 3.1 - Prob. 8PQCh. 3.1 - Prob. 9PQCh. 3.1 - Convert the following to decimal fractions (do not...
Ch. 3.1 - Prob. 11PQCh. 3.1 - Prob. 12PQCh. 3.1 - Prob. 13PQCh. 3.1 - Prob. 1EPQCh. 3.1 - Prob. 2EPQCh. 3.1 - Prob. 3EPQCh. 3.1 - Prob. 4EPQCh. 3.1 - Prob. 5EPQCh. 3.1 - Prob. 6EPQCh. 3.1 - Prob. 7EPQCh. 3.1 - Prob. 8EPQCh. 3.1 - Prob. 9EPQCh. 3.1 - Prob. 10EPQCh. 3.1 - Prob. 11EPQCh. 3.1 - Prob. 12EPQCh. 3.1 - Prob. 13EPQCh. 3.1 - Prob. 1AHCh. 3.1 - Prob. 2AHCh. 3.1 - Prob. 3AHCh. 3.1 - Prob. 4AHCh. 3.1 - Prob. 5AHCh. 3.1 - Prob. 6AHCh. 3.1 - Prob. 7AHCh. 3.1 - Bill Breen earned $1,555, and his employer...Ch. 3.1 - At the local college, .566 of the students are...Ch. 3.1 - Prob. 10AHCh. 3.1 - Prob. 11AHCh. 3.1 - Prob. 12AHCh. 3.1 - Michael Sullivan was planning his marketing...Ch. 3.1 - Prob. 14AHCh. 3.2 - Rearrange vertically and add:
14, .642, 9.34,...Ch. 3.2 - Prob. 2PQCh. 3.2 - Prob. 3PQCh. 3.2 - Prob. 4PQCh. 3.2 - Prob. 5PQCh. 3.2 - Complete by the shortcut method:
9,680÷1,000
Ch. 3.2 - Prob. 7PQCh. 3.2 - Prob. 8PQCh. 3.2 - Prob. 9PQCh. 3.2 - Prob. 10PQCh. 3.2 - Prob. 1EPQCh. 3.2 - Prob. 2EPQCh. 3.2 - Prob. 3EPQCh. 3.2 - Divide and round to the nearest hundredth:
3,824 ÷...Ch. 3.2 - Prob. 5EPQCh. 3.2 - Prob. 6EPQCh. 3.2 - Prob. 7EPQCh. 3.2 - Prob. 8EPQCh. 3.2 - Prob. 9EPQCh. 3.2 - Round to the nearest cent as needed:
A trip to...Ch. 3.2 - Prob. 1AHCh. 3.2 - Prob. 2AHCh. 3.2 - Prob. 3AHCh. 3.2 - Prob. 4AHCh. 3.2 - Prob. 5AHCh. 3.2 - Prob. 6AHCh. 3.2 - Jeanne Allyn purchased 12.25 yards of ribbon for a...Ch. 3.2 - Prob. 8AHCh. 3.2 - Prob. 9AHCh. 3.2 - Prob. 10AHCh. 3.2 - Prob. 11AHCh. 3 - Prob. 1ECPCh. 3 - Identify the place value for the following:
Ch. 3 - Prob. 3ECPCh. 3 - Prob. 4ECPCh. 3 - Prob. 5ECPCh. 3 - Prob. 6ECPCh. 3 - Prob. 7ECPCh. 3 - Round the following as indicated: LU...Ch. 3 - Prob. 9ECPCh. 3 - Prob. 10ECPCh. 3 - Convert the following types of decimal fractions...Ch. 3 - Convert the following types of decimal fractions...Ch. 3 - Convert the following types of decimal fractions...Ch. 3 - Convert the following types of decimal fractions...Ch. 3 - Prob. 15ECPCh. 3 - Prob. 16ECPCh. 3 - Prob. 17ECPCh. 3 - Prob. 18ECPCh. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following decimals to fractions. Do...Ch. 3 - Convert the following to mixed numbers. Do not...Ch. 3 - Convert the following to mixed numbers. Do not...Ch. 3 - Prob. 28ECPCh. 3 - Prob. 29ECPCh. 3 - Prob. 30ECPCh. 3 - Write the decimal equivalent of the following: LU...Ch. 3 - Prob. 32ECPCh. 3 - Rearrange the following and add: LU 3-2(1)
115,...Ch. 3 - Prob. 34ECPCh. 3 - Prob. 35ECPCh. 3 - Prob. 36ECPCh. 3 - Prob. 37ECPCh. 3 - Prob. 38ECPCh. 3 - Prob. 39ECPCh. 3 - Prob. 40ECPCh. 3 - Prob. 41ECPCh. 3 - Prob. 42ECPCh. 3 - Prob. 43ECPCh. 3 - Prob. 44ECPCh. 3 - Prob. 45ECPCh. 3 - Prob. 46ECPCh. 3 - Divide the following and round to the nearest...Ch. 3 - Prob. 48ECPCh. 3 - Prob. 49ECPCh. 3 - Prob. 50ECPCh. 3 - Prob. 51ECPCh. 3 - Prob. 52ECPCh. 3 - Prob. 53ECPCh. 3 - Complete these multiplications and divisions by...Ch. 3 - Prob. 55ECPCh. 3 - Prob. 56ECPCh. 3 - Prob. 57ECPCh. 3 - Prob. 58ECPCh. 3 - Prob. 59ECPCh. 3 - Prob. 60ECPCh. 3 - Prob. 61ECPCh. 3 - Prob. 62ECPCh. 3 - WORD PROBLEMS
As needed, round answers to the...Ch. 3 - Prob. 64ECPCh. 3 - Prob. 65ECPCh. 3 - Prob. 66ECPCh. 3 - As needed, round answers to the nearest cent.
The...Ch. 3 - Prob. 68ECPCh. 3 - As needed, round answers to the nearest cent.
Mark...Ch. 3 - Prob. 70ECPCh. 3 - As needed, round answers to the nearest cent.
Bob...Ch. 3 - Prob. 72ECPCh. 3 - Prob. 73ECPCh. 3 - Prob. 74ECPCh. 3 - As needed, round answers to the nearest cent.
Paul...Ch. 3 - Prob. 76ECPCh. 3 - Prob. 77ECPCh. 3 - Prob. 78ECPCh. 3 - Prob. 79ECPCh. 3 - Prob. 80ECPCh. 3 - Prob. 81ECPCh. 3 - Prob. 82ECPCh. 3 - Prob. 83ECPCh. 3 - Prob. 84ECPCh. 3 - Prob. 85ECPCh. 3 - Prob. 86ECPCh. 3 - Jill and Frank decided to take a long weekend in...Ch. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Convert the following fractions to decimals (or...Ch. 3 - Rearrange the following decimals and add.
5.93,...Ch. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 20PTCh. 3 - Prob. 21PTCh. 3 - Prob. 22PTCh. 3 - Prob. 23PTCh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CR
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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.arrow_forward(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).arrow_forwardfind the domain of the function f(x)arrow_forward
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