Soluons Manual for - Introduc�on to Management Science A Modeling ...

Solu�ons Manual for Introduc�on to Management Science A Modeling and Case Studies Approach with Spreadsheets, 6e Frederick.Hillier, Mark Hillier (All Chapters, 100% Original Verified A+ Grade)

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CHAPTER 1

INTRODUCTION

Review Questions 1.1-1 The rapid development of the discipline began in the 1940’s and 1950’s.

1.1-2 The traditional name given to the discipline is operations research.

1.1-3 A management science study provides an analysis and recommendations, based on the quantitative factors involved in the problem, as input to the managers.

1.1-4 Management science is based strongly on some scientific fields, including mathematics and computer science. It also draws upon the social sciences, especially economics.

1.1-5 A decision support system is an interactive computer-based system that aids managerial decision- making. The system draws current data from databases or management information systems and then solves the various versions of the model specified by the manager.

1.1-6 Many managerial problems revolve around such quantitative factors as production quantities, revenues, costs, the amounts available of needed resources, etc.

1.2-1 The production and sales volume needs to exceed the break-even point to make it worthwhile to introduce a product.

1.2-2 The number of watches produced cannot be less than 0, nor should it exceed the number that can be sold. Also, the objective is to make the decision that maximizes the company’s profit.

1.2-3 The purpose of what-if analysis is to check the effect on the recommendations of a model if the estimates turn out to be wrong.

1.2-4 Simply enter a variety of new values and see what happens.

1.2-5 The MIN(a, b) function gives the minimum of a and b.

1.2-6 The IF(a, b, c) function returns b if a is true, otherwise it returns c.

1.3-1 Mathematics, statistics, computer science, data science, industrial engineering, are some of the quantitative decision sciences included within analytics.

1.3-2 Descriptive analytics involves analyzing data to identify interesting patterns in order to describe and understand what is going on now.

1.3-3 Predictive analytics involves applying predictive models to historical data and perhaps external data to predict future events or trends.

1.3-4 Prescriptive analytics involves applying sophisticated models to the data to prescribe what should be done in the future.

1.3-5 Management science focuses mainly on predictive and prescriptive analytics. 2 / 4

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1.3-6 Descriptive analytics draws mainly from quantitative decision sciences such as statistics and data mining rather than from management science.

Problems 1.1 If Q units are produced per month, then Monthly Profit = $0 {if Q = 0} and –$20,000 + ($20 – $10)Q {if Q > 0}.Break-even point = $20,000 / ($20 – $10) = 2000,

so it will be profitable to produce if Q > 2000.

1.2 a) Let Q be the number of units produced and sold. Then Monthly Profit = $0 {if Q = 0} and –$500,000 + ($35 – $15)Q {if Q > 0}.Break-even point = $500,000 / ($35 – $15) = 25,000.

b) Let Q be the number produced and s the number that can be sold. Then

Profit = [0 if Q = 0] and [-$500,000 + $35 * MIN(Q, s) – $15Q if Q > 0].c)

d) Q ≤ s.

1.3 a) $30,000,000

• $1,666.67
• $1,333.33 3 / 4

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1.4 a)

b) Break-even point = ($10,000,000) / ($1700 – $1300) = 25,000.

c) Maximize Profit = $0 {if Q = 0} and –$10,000,000 + $400Q {if Q > 0}

subject to 0 ≤ Q ≤ s.d)

e)

10,000 20,000 30,000 Q

$10 million $20 million $30 million $40 million $50 million Revenue = $1700Q Cost = $10,000,000

+ $1300Q

Break-even point = 25,000 units 1 2 3 4 5 6 7

AB C DE

DataResults Unit Revenue$1,700 Total Revenue$51,000,000 Fixed Cost$10,000,000 Total Fixed Cost$10,000,000 Marginal Production Cost$1,300 Total Variable Cost$39,000,000 Sales Forecast30,000 Profit (Loss)$2,000,000 Production Quantity30,000 Break-Even Point25,000 1 2 3 4 5 6 7

AB C DE

DataResults Unit Revenue$1,700 Total Revenue $0 Fixed Cost$10,000,000 Total Fixed Cost $0 Marginal Production Cost$1,300 Total Variable Cost$0 Sales Forecast20,000 Profit (Loss)$0 Production Quantity 0 Break-Even Point25,000

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