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Slide 2005 Thomson/South-Western

Chapter 4Linear Programming Applications

Blending Problem Portfolio Planning Problem

Product Mix Problem

Transportation Problem

Data Envelopment Analysis Revenue Management

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Make-or-Buy Decisions , P.150

The Janders Company markets various business and

engineering product across Europe. Janders is preparingtwo new PADs (Personal Digital Assistant): one for the

business market called the Financial Manager and one for

the engineering market call the Technician. Each PDA has

three components: a base, an electronic cartridge, and afaceplate or top. The same base is used for both products

but the cartridges and tops are different. All components

can be manufactured by the company or purchased from

outside suppliers.

The manufacturing costs and purchase prices for thecomponents are summarized in the following table.

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Cost per Unit,

Component Manufacture (regular

time)

Purchase

Base 0.50 0.60

Financial cartridge 3.75 4.00

Technician cartridge 3.30 3.90

Financial top 0.60 0.65

Technician top 0.75 0.78

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Company forecasters indicate that 3000 Financial

Managers PDAs and 2000 Technicians PDAs will beneeded for the next production period. However,manufacturing capacity is limited. The company has200 hours of regular manufacturing time and 50

hours of overtime that can be scheduled for thecalculators. Overtime involves a premium at theadditional cost of 9 per hour.

The next table shows manufacturing times (in

minutes) for the components

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The management wants to know how much of each

several component parts a company should manufacture

and how much it should purchase from an outside supplier

Required

Develop a model that can be used to assist themanagement in decision making.

Component Manufacturing time (minutes)

Base 1.0

Financial cartridge 3.0Technician cartridge 2.5

Financial top 1.0

Technician top 1.5

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Blending, P.167

The Delta Oil Company (DOC) operates in Nigeria and

runs an oil refinery that blends three different petroleumcomponents into two different fuels. The fuels are sold onto fuel companies around the world depending on demandand worldwide fuel prices. The company calculates its

costs and profits using the US$. The company is trying toplan its daily production. Currently DOC estimates it cansell its regular fuel at $1 per litre and its premium fuel at$1.08 per litre. The cost of the three petroleum componentsare shown in the following table

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7/137Slide 2005 Thomson/South-Western

Petroleum component Cost/litre Maximum available

1 $0.50 5,000 litres

2 $0.60 10,000 litres

3 $0.84 10,000 litresProduct specifications for the regular and premium fuels restrict the

amounts of each component that can be used in each gasoline

product. These restrictions are shown in the following table.

Product Specifications

Regular Fuel At most 30% component 1

At least 40% component 2

At most 20% component 3

Premium Fuel At least 25% component 1At most 40% component 2

At least 30% component 3

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Current commitments to customers require DOC toproduce at least 10,000 litres of regular fuel each day.

Required

Develop a model that can be used to assist themanagement in decision making.

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Portfolio Selection, P.180

Welte Mutual Fund just obtained

100,000 byconverting industrial bonds to cash and is now

looking for other investment opportunities for these

funds. Based on Weltes current investments, the

firms top financial analyst recommends that all the

new investments be made in the oil industry, steel

industry or in government bonds. Specifically, the

analyst identified five investment opportunities and

projected their annual rates of return. The

investments and rates of return are presented in thefollowing table.

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Management of Welte imposed the following investment

guidelines.1- Neither industry (oil or steel) should receive more than

50,000.

2- Government bonds should be at least 25 per cent of the

steel industry investments.

3- the investment in Pacific Oil, the high-risk investment,

cannot be more than 60 per cent of the total oil industry

investment.

Investment Projected rate of return

Atlantic Oil 7.3

Pacific Oil 10.3

Midwest Steel 6.4Hiber Steel 7.5

Government bonds 4.5

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Data Envelopment Analysis

The management of County Hospital wishes to compare thehospital relative performance against the performance ofother hospitals in the same city. The following table indicatethe inputs and outputs data.

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Develop a linear programming model that can

be used to evaluate the performance of the

County hospital

Hospital

General University County City

Inputs

Full Time staff 285.2 162.3 275.7 210.4Supply Cost 123.8 128.7 348.5 154.1

Bed days available 106.72 64.21 104.1 104.04

Outputs

Number of in-patient 48.14 34.62 36.72 33.16Outpatient treated 43.1 27.11 45.98 56.46

Nurses trained 253 148 175 160

Paramedics trained 41 27 23 84

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End of Chapter 4

ms12 04 (1)

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