Bradford Electronics produces a variety of DVD drives for installation into home-use DVD players. Bradford can assemble DVD drives on any or all five production stations, some of which are more automated than others, and thus, have lower variable costs of assembly but require higher one-time setup costs to convert to assembling a particular model of DVD drive. Bradford has received an order for assembling 2,500 DVD drives of a particular model.

Assembly Variable Assembly Capacity In Setup Cost

Station Cost/DVD Drive DVD Drives

1 $62 500 $12,000

2 $68 600 $ 6,000

3 $72 700 $ 3,000

4 $78 450 $ 1,500

5 $85 1000 $ 500

Given the setup costs, capacities and variables assembly costs at each of the five production stations in the above table:

(a) Formulate this problem algebraically as an integer/binary programming model.

(b) Use Excel Solver to determine how many DVD drives should be assembled at each of the five production stations to minimize total costs?

Problem 2

BACKGROUND

Chris’ firm, Tennessee Oil Ventures Inc. (TOVI), has $12,400,000 to invest in oil drilling exploration in the Gulf of Mexico over the next 5 years. Six investment opportunities have arisen since the latest round of hurricanes took out some production capacity in the Gulf. Table 1 displays the details of the six investments.

Table 1 Investment Details

Capital (in $000) required per year

Investment/

Project Expected

NPV ($000)

Year 1

Year 2

Year 3

Year 4

Year 5

1

2

3

4

5

6 $2700

$3330

$7010

$5770

$2900

$4870 $ 975

$1200

$2500

$1550

$1400

$1900 $ 350

$ 200

$1200

$1350

$ 350

$1900 $ 200

$ 200

$ 850

$ 675

$87.5

$ 350 $ 100

$ 200

$ 400

$ 337.5

$ 21.875

$ 350 $ 50

$ 200

$ 400

$168.75

$ 0

$ 350

The $12,400,000 in investment capital is spread over the 5 years as follows:

Capital (in $000) allocated per year

Year 1 Year 2 Year 3 Year 4 Year 5

$ 5800 $ 3500 $ 1300 $ 900 $ 900

PROBLEM AT HAND

Chris had just finished looking at the six investment/projects that made it past the engineers and accountants. Although all the investments/projects look good (positive NPV), Chris knows TOVI cannot pick all of them since there is not enough money (i.e., capital) to go around. Chris and in turn TOVI must determine which of the investments/projects to accept to maximize potential NPV but yet stay within company capital budgets. However, a few caveats have cropped up regarding some federal and state laws regarding these projects.

1. Surplus capital funds in any year cannot be carried over from year to year.

2. If TOVI decides to invest in the second investment/project, it must also invest in the fourth.

3. If TOVI decides to invest in the first investment/project, it cannot invest in the fifth investment/project.

DISCUSSION QUESTIONS

(a) Help Chris and his firm, TOVI, solve this problem by defining the parts of an Integer Linear Programming, constructing an Integer Linear Programming model in algebraic form, and using Excel’s Solver to find a solution.

(b) What projects should Chris and his firm invest in? How much capital do they use? Why are certain projects being left out?

Problem 3

Harris Segal, Marketing director for the Upper Canada Power Corporation is about to begin an advertising campaign promoting energy conversation. In trying to budget between television and newspaper advertisements, he sets the following goals and assigns the weights shown.

1. The total advertising budget of $120,000 should not be exceeded. Weight = 100

2. There should be a mix of TV and newspaper ads, with at least 10 TV spots (costing $5,000 each) and at least 20 newspaper ads (costing $2,000 each). Weight = 75 each.

3. The total number of people to read or hear the advertisements should be at least 9 million. Weight = 40 per 100,000

Each television spot reaches approximately 300,000 people. A newspaper advertisement is read by about 150,000 persons.

(a) Formulate Segal’s goal programming problem in algebraic form to find out how many of each type of ad to place.

(b) Solve using Excel Solver to find out how many of each type of ad to place. How many people, in total, will read or hear the advertisements?

Assembly Variable Assembly Capacity In Setup Cost

Station Cost/DVD Drive DVD Drives

1 $62 500 $12,000

2 $68 600 $ 6,000

3 $72 700 $ 3,000

4 $78 450 $ 1,500

5 $85 1000 $ 500

Given the setup costs, capacities and variables assembly costs at each of the five production stations in the above table:

(a) Formulate this problem algebraically as an integer/binary programming model.

(b) Use Excel Solver to determine how many DVD drives should be assembled at each of the five production stations to minimize total costs?

Problem 2

BACKGROUND

Chris’ firm, Tennessee Oil Ventures Inc. (TOVI), has $12,400,000 to invest in oil drilling exploration in the Gulf of Mexico over the next 5 years. Six investment opportunities have arisen since the latest round of hurricanes took out some production capacity in the Gulf. Table 1 displays the details of the six investments.

Table 1 Investment Details

Capital (in $000) required per year

Investment/

Project Expected

NPV ($000)

Year 1

Year 2

Year 3

Year 4

Year 5

1

2

3

4

5

6 $2700

$3330

$7010

$5770

$2900

$4870 $ 975

$1200

$2500

$1550

$1400

$1900 $ 350

$ 200

$1200

$1350

$ 350

$1900 $ 200

$ 200

$ 850

$ 675

$87.5

$ 350 $ 100

$ 200

$ 400

$ 337.5

$ 21.875

$ 350 $ 50

$ 200

$ 400

$168.75

$ 0

$ 350

The $12,400,000 in investment capital is spread over the 5 years as follows:

Capital (in $000) allocated per year

Year 1 Year 2 Year 3 Year 4 Year 5

$ 5800 $ 3500 $ 1300 $ 900 $ 900

PROBLEM AT HAND

Chris had just finished looking at the six investment/projects that made it past the engineers and accountants. Although all the investments/projects look good (positive NPV), Chris knows TOVI cannot pick all of them since there is not enough money (i.e., capital) to go around. Chris and in turn TOVI must determine which of the investments/projects to accept to maximize potential NPV but yet stay within company capital budgets. However, a few caveats have cropped up regarding some federal and state laws regarding these projects.

1. Surplus capital funds in any year cannot be carried over from year to year.

2. If TOVI decides to invest in the second investment/project, it must also invest in the fourth.

3. If TOVI decides to invest in the first investment/project, it cannot invest in the fifth investment/project.

DISCUSSION QUESTIONS

(a) Help Chris and his firm, TOVI, solve this problem by defining the parts of an Integer Linear Programming, constructing an Integer Linear Programming model in algebraic form, and using Excel’s Solver to find a solution.

(b) What projects should Chris and his firm invest in? How much capital do they use? Why are certain projects being left out?

Problem 3

Harris Segal, Marketing director for the Upper Canada Power Corporation is about to begin an advertising campaign promoting energy conversation. In trying to budget between television and newspaper advertisements, he sets the following goals and assigns the weights shown.

1. The total advertising budget of $120,000 should not be exceeded. Weight = 100

2. There should be a mix of TV and newspaper ads, with at least 10 TV spots (costing $5,000 each) and at least 20 newspaper ads (costing $2,000 each). Weight = 75 each.

3. The total number of people to read or hear the advertisements should be at least 9 million. Weight = 40 per 100,000

Each television spot reaches approximately 300,000 people. A newspaper advertisement is read by about 150,000 persons.

(a) Formulate Segal’s goal programming problem in algebraic form to find out how many of each type of ad to place.

(b) Solve using Excel Solver to find out how many of each type of ad to place. How many people, in total, will read or hear the advertisements?

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