
EBK CONTEMPORARY MATHEMATICS FOR BUSINE
8th Edition
ISBN: 9781305888715
Author: Brechner
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 2.II, Problem 12TIE
To determine
To calculate: The subtraction of the fractions,
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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.
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.
Chapter 2 Solutions
EBK CONTEMPORARY MATHEMATICS FOR BUSINE
Ch. 2.I - For each of the following, identify the type of...Ch. 2.I - Prob. 2TIECh. 2.I - Convert the following mixed numbers to improper...Ch. 2.I - Prob. 4TIECh. 2.I - Prob. 5TIECh. 2.I - Prob. 6TIECh. 2.I - Prob. 1RECh. 2.I - Prob. 2RECh. 2.I - Prob. 3RECh. 2.I - Prob. 4RE
Ch. 2.I - Prob. 5RECh. 2.I - Prob. 6RECh. 2.I - Prob. 7RECh. 2.I - Prob. 8RECh. 2.I - Prob. 9RECh. 2.I - Prob. 10RECh. 2.I - Prob. 11RECh. 2.I - Prob. 12RECh. 2.I - Prob. 13RECh. 2.I - Prob. 14RECh. 2.I - Prob. 15RECh. 2.I - Prob. 16RECh. 2.I - Prob. 17RECh. 2.I - Use inspection or the greatest common divisor to...Ch. 2.I - Use inspection or the greatest common divisor to...Ch. 2.I - Prob. 20RECh. 2.I - Prob. 21RECh. 2.I - Prob. 22RECh. 2.I - Prob. 23RECh. 2.I - Use inspection or the greatest common divisor to...Ch. 2.I - Use inspection or the greatest common divisor to...Ch. 2.I - Prob. 26RECh. 2.I - Prob. 27RECh. 2.I - Prob. 28RECh. 2.I - Prob. 29RECh. 2.I - Raise the following fractions to higher terms as...Ch. 2.I - Prob. 31RECh. 2.I - Raise the following fractions to higher terms as...Ch. 2.I - Prob. 33RECh. 2.I - Prob. 34RECh. 2.I - Prob. 35RECh. 2.I - Prob. 36RECh. 2.I - Prob. 37RECh. 2.I - Raise the following fractions to higher terms as...Ch. 2.I - Raise the following fractions to higher terms as...Ch. 2.I - SECTION I – UNDERSTANDING AND WORKING WITH...Ch. 2.I - Prob. 41RECh. 2.I - Section I • Understanding and working with...Ch. 2.I - Section I Understanding and working with...Ch. 2.I - Section I • Understanding and working with...Ch. 2.II - Determine the least common denominator of the...Ch. 2.II - Prob. 8TIECh. 2.II - Prob. 9TIECh. 2.II - Prob. 10TIECh. 2.II - Prob. 11TIECh. 2.II - Prob. 12TIECh. 2.II - Prob. 13TIECh. 2.II - Prob. 1RECh. 2.II - Prob. 2RECh. 2.II - Prob. 3RECh. 2.II - Prob. 4RECh. 2.II - Prob. 5RECh. 2.II - Prob. 6RECh. 2.II - Prob. 7RECh. 2.II - Prob. 8RECh. 2.II - Prob. 9RECh. 2.II - Prob. 10RECh. 2.II - Prob. 11RECh. 2.II - Prob. 12RECh. 2.II - Prob. 13RECh. 2.II - Prob. 14RECh. 2.II - Prob. 15RECh. 2.II - Prob. 16RECh. 2.II - Prob. 17RECh. 2.II - Crate and Barrel shipped three packages to New...Ch. 2.II - Prob. 19RECh. 2.II - BrewMasters Coffee Co. purchased 1212 tons of...Ch. 2.II - Prob. 21RECh. 2.II - Prob. 22RECh. 2.II - Prob. 23RECh. 2.II - Subtract the following fractions and reduce to...Ch. 2.II - Prob. 25RECh. 2.II - Prob. 26RECh. 2.II - Prob. 27RECh. 2.II - Prob. 28RECh. 2.II - Prob. 29RECh. 2.II - A particular dress requires 314 yards of fabric...Ch. 2.II - 31. Robert Burkart bought a frozen,...Ch. 2.II - 32. Brady White weighed pounds when he decided to...Ch. 2.II - Prob. 33RECh. 2.II - Tim Kenney, a painter, used 645 gallons of paint...Ch. 2.II - You are an executive with the Varsity Corporation...Ch. 2.III - Multiply and reduce to lowest terms.
Ch. 2.III - Multiply and reduce to lowest terms.
a. b.
Ch. 2.III - Divide the following fractions and mixed...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - Multiply the following fractions and reduce to...Ch. 2.III - 13. A recent market research survey showed that ...Ch. 2.III - 14. Wendy Wilson planned to bake a triple recipe...Ch. 2.III - A driveway requires 912 truckloads of gravel. If...Ch. 2.III - Melissa Silva borrowed $4,200 from the bank. If...Ch. 2.III - Amy Richards movie collection occupies 58 of her...Ch. 2.III - Three partners share a business. Max owns 38,...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Divide the following fractions and reduce to...Ch. 2.III - Frontier Homes, Inc., a builder of custom homes,...Ch. 2.III - An automobile travels 365 miles on 1623 gallons of...Ch. 2.III - 33. Pier 1 Imports purchased 600 straw baskets...Ch. 2.III - 34. At the Cattleman’s Market, pounds of...Ch. 2.III - 35. Super Value Hardware Supply buys nails in bulk...Ch. 2.III - The chef at the Sizzling Steakhouse has 140 pounds...Ch. 2.III - Regal Reflective Signs makes speed limit signs for...Ch. 2.III - 38. Engineers at Triangle Electronics use special...Ch. 2.III - 39. At Celtex Manufacturing, a chemical etching...Ch. 2.III - 40. You are the owner of The Gourmet Diner. On...Ch. 2 - 1. In fractions, the number above the division...Ch. 2 - 2. The numerator of a proper fraction is...Ch. 2 - To convert an improper fraction to a whole or...Ch. 2 - 4. To convert a mixed number to an improper...Ch. 2 - Prob. 5CRCh. 2 - Prob. 6CRCh. 2 - Prob. 7CRCh. 2 - Prob. 8CRCh. 2 - Prob. 9CRCh. 2 - Prob. 10CRCh. 2 - Prob. 11CRCh. 2 - Prob. 12CRCh. 2 - Prob. 13CRCh. 2 - Prob. 14CRCh. 2 - Identify the type of fraction and write it in word...Ch. 2 - Prob. 2ATCh. 2 - Prob. 3ATCh. 2 - Prob. 4ATCh. 2 - Prob. 5ATCh. 2 - Prob. 6ATCh. 2 - Prob. 7ATCh. 2 - Prob. 8ATCh. 2 - Prob. 9ATCh. 2 - Convert to higher terms as indicated.
10. to...Ch. 2 - Prob. 11ATCh. 2 - Prob. 12ATCh. 2 - Prob. 13ATCh. 2 - Prob. 14ATCh. 2 - Prob. 15ATCh. 2 - Prob. 16ATCh. 2 - Prob. 17ATCh. 2 - Prob. 18ATCh. 2 - Prob. 19ATCh. 2 - Prob. 20ATCh. 2 - 21. The Bean Counters, an accounting firm, has 161...Ch. 2 - Ventura Coal mined 623 tons on Monday, 734 tons on...Ch. 2 - 23. A blueprint of a house has a scale of 1 inch...Ch. 2 - If 38 of a 60-pound bag of ready-mix concrete is...Ch. 2 - Prob. 25ATCh. 2 - 26. During a spring clearance sale, Sears...Ch. 2 - You are a sales representative for Boaters...Ch. 2 - 28. A developer owns three lots measuring acres...Ch. 2 - 29. A house has 4,400 square feet. The bedrooms...Ch. 2 - 30. Among other ingredients, a recipe for linguini...Ch. 2 - You are an engineer with Ace Foundations, Inc....
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