SubjectPageCacheKey

AmazonPublisherAudienceV2[default,ads]

AddFilterDataToSubjectPageTitles

StudierCountFunctionAndBoostImprovements[default,search]

DisableFlipAndShimmyOnMWeb

SubjectPagePaginationFancy

ExpertSolutionsRatingsOnSearch

PhoneNumberSignUpFakeDoor[default,growth]

TermSearchPrefixTest[default,search]

SubjectPageTextbookPublisherFilter

BlendedResultsHeuristicShelfOrdering[default,search]

QuestionPageAds[default,subscriptions,growth,ads]

TextbookQueryStopwordRemoval[default,search]

LoSetPageBlurredDefinitionsV2[default,growth,ads]

IndexParamTestV2[default,search]

TextbookMetRobotsNoindexV2

DisplayAnswerDateOnExpertSolutions

DisplayCreatedDateOnStudySets

EnableApsOutstream[default,ads]

BlendedResultsRandomShelfOrdering[default,search]

LoadAdScriptsWithLowerPriority[default,ads]

TextbookSolutionsTOCTitleTagFreeV2

AddISBNToTextbookCardsV2

TextbookSolutionsDescriptionTagPaid

TextbookSolutionsDescriptionTagFree

ExplanationsUnmetered

MiniFCV2[default,ads,engagement,growth]

SetPageRenderer[default,ads,growth,subscriptions]

MiniFCSetsRendererLOv2[default,ads,growth,subscriptions]

LOHNewMarketingPageFRFR

LOHNewMarketingPageDE

ExplanationsSignUpPlacementV2[default,growth,subs]

EnableHeaderBiddingOutstream[default,ads]

FlashcardsStudyLoopRedesignAdsV2[default,ads]

SearchCourseFiltering[default,search]

DisableBiddingV5[default,ads]

ExplanationsSignupBlur[default,subscriptions,growth]

RendererExplanationsHoldout[default,ads,growth,subscriptions]

MLFlooringPredictions[default,ads]

SearchMisspellingsV4[default,search]

GlobalNavRedesign[default,search,subscriptions,engagement]

RenderAdsOnBlendedResultsV2[default,search,ads]

MarketingUTMDirectToSub[default,subscriptions]

CoursePageSearch[default,ads]

PreloadFonts

DynamicFlooringV6Train[default,ads]

AdLightningScriptHoldOut[default,ads]

SignupAssemblificationV4[default,growth]

ZuoraOutageFallback[default,subscriptions]

OpenWrapIdentityHubSolutionsHoldbackV2[default,ads]

TeacherReferralsLanding[default,growth]

SimplifiedSetPageTest

adsHoldOut_20180315

FlashcardsHintWithFlip[default,growth]

SurveyFakeDoor[default,growth]

UseBehavioralSetRecommendations[default,ads]

ExpertSolutionsRatings

CopyABTestModesCardsSignupTitleekNma

CopyABTestGlobalSignUpModalImageTextySeEH

CopyABTestReferralsReferrerSharePagePageTitleauNkT

CopyABTestExplanationsTableOfContentsMenuSolutionsHeaderAqX6F

CopyABTestSubjectPagesContentTypeHomeworkHelprnHrq

CopyABTestSearchViewsBlendedResultsHeaderTitleStudySetsFAfFc

Renderer/index

Find step-by-step solutions and answers to Introduction to Operations Research - 9780073523453, as well as thousands of textbooks so you can move forward with confidence.

Introduction to Operations Research - 10th Edition - Solutions and Answers

Introduction to Linear Programming

Problems 3.3

The assumption of proportionality is satisfied because all of the variables in all of the functions in this problems are having exponent $1$, i.e. the contribution of each activity of each functional constraint is proportional to the level of that particular activity, and similarly, each activity to the value of the objective function is proportional to the level of that same activity.

The assumption of additivity is satistfied because each of the given functions, be it objective or constraint functions, are the sum of individual contributions of the respective activities, i.e. there are no joint terms in either of those functions.

The assumption of divisibility is satisfied, because any values, including noninteger values, that satisfy those constraints are allowed in this problem, as we can come in at any fraction of the partnership that we want.

The assumption of certainty is also satisfied because the value assigned to each parameter in this problem is a known constant.

For example, when we fix the values of $x_2$ to be $0,1$ or $2$, and increase the value of $x_1$ the value of $Z$ increases proportionaly by $3,4$ and $5$, respectively. Similarly, when we fix the values of $x_1$ to be $0,1$ and $2$ and increase the value of $x_2$, the value of $Z$ increases proportionaly by $4,5$ and $6$ respectively.

The assumption of additivity is violated because the value of the objective function $Z$ isn't just the sum of individual contributions of the respective activities - there might be a joint term present:
$$\begin{align*}
    (x_1,x_2) &= (1,0) \Rightarrow Z = 3\\
    (x_1,x_2) &= (0,1) \Rightarrow Z = 4\\
    (x_1,x_2) &= (1,1) \Rightarrow Z = 8 \neq 7\\
\end{align*}

The assumption of divisibility is also violated because for each variable, the permissible values are only $0,1$ and $2$, as opposed to all values, including noninteger ones, that satisfy given constraints.

The assumption of certainty is satisfied because the value assigned to each parameter in this problem is a known constant.

Duality Theory

Problems 6.1

$\textbf{a)}$This statement is true. If the primal problem has $m$ functional constraints and $n$ variables, its dual problem will have $n$ functional constraints and $m$ variables, thus making the sum of both being equal to $m+n$.


$\textbf{b)}$ This statement is false. By weak and strong duality properties, we know that those values are equal only at optimality, thus this is impossible to accomplish.

$\textbf{c)}$ This statement is false. If the primal problem has an unbounded objective function, then the dual problem has no feasible solutions.

Introduction

Problems 2.1

Problems 2.2

Problems 2.3

Problems 2.5

Problems 2.6

Problems 2.7

Problems 2.4

Overview of the Operations Research Modeling Approach

Problems 3.1

Problems 3.2

Problems 3.4

Problems 3.5

Problems 3.6

Problems 3.7

Problems 4.1

Problems 4.2

Problems 4.3

Problems 4.4

Problems 4.5

Problems 4.6

Problems 4.7

Problems 4.9

Solving Linear Programming Problems: The Simplex Method

Problems 5.1

Problems 5.2

Problems 5.3

Problems 5.4

The Theory of the Simplex Method

Problems 6.2

Problems 6.3

Problems 6.4

Problems 6.5

Problems 7.1

Problems 7.2

Problems 7.3

Problems 7.4

Problems 7.5

Problems 7.6

Linear Programming Under Uncertainty

Problems 8.1

Problems 8.2

Problems 8.3

Problems 8.4

Other Algorithms for Linear Programming

Problems 9.1

Problems 9.2

Problems 9.3

Problems 9.4

The Transportation and Assignment Problems

Problems 10.3

Problems 10.5

Problems 10.4

Problems 10.6

Problems 10.7

Problems 10.8

Problems 10.9

Network Optimization Models

Problems 11.2

Problems 11.3

Problems 11.4

Dynamic Programming

Problems 12.1

Problems 12.2

Problems 12.3

Problems 12.4

Problems 12.5

Problems 12.6

Problems 12.7

Problems 12.8

Problems 12.9

Integer Programming

Problems 13.1

Problems 13.2

Problems 13.3

Problems 13.4

Problems 13.6

Problems 13.5

Problems 13.7

Problems 13.8

Problems 13.9

Nonlinear Programming

Problems 14.1

Problems 14.2

Problems 14.3

Problems 14.4

Problems 14.5

Metaheuristics

Problems 15.1

Problems 15.2

Problems 15.3

Problems 15.4

Problems 15.5

Game Theory

Problems 16.2

Problems 16.3

Problems 16.4

Problems 16.5

Problems 16.6

Decision Analysis

Problems 17.2

Problems 17.3

Problems 17.4

Problems 17.5

Problems 17.6

Problems 17.7

Problems 17.8

Problems 17.9

Problems 17.1

Problems 17.11

Queueing Theory

Problems 18.3

Problems 18.4

Problems 18.5

Problems 18.6

Problems 18.7

Problems 18.8

Problems 18.9

Inventory Theory

Problems 19.2

Markov Decision Processes

Introduction to Operations Research

Introduction to Operations Research

Textbook solutions

Chapter 1:

Chapter 2:

Chapter 3:

Chapter 4:

Chapter 5:

Chapter 6:

Chapter 7:

Chapter 8:

Chapter 9:

Chapter 10:

Chapter 11:

Chapter 12:

Chapter 13:

Chapter 14:

Chapter 15:

Chapter 16:

Chapter 17:

Chapter 18:

Chapter 19:

Chapter 20: