A Civil Engineering firm is planning to bid on a number of projects over the nex

Question

A Civil Engineering firm is planning to bid on a number of projects over the next two years. The projects available for them, along with the expected profit and number of engineers needed for each project is shown in the table below.

Project

Department

Expected Profit

(x 100,000)

Engineers needed

1. Northampton water plant.

Environmental

$8

3

2. Blanford water plant.

Environmental

$2

2

3. Springfield compost facility.

Environmental

$1

1

4. Ludlow Bridge

Structures

$6

5

5. Longmeadow municipal building

Structures

$5

4

6. Ludlow traffic safety plan

Transportation

$3

2

7. Williamstown bike trail.

Transportation

$1.2

1

There are some constraints on the projects to be bid on:

a.A total of 10 engineers are available at the firm.

b.At least one project should be selected in each department (Environmental, Structures and Transportation).

c.At most one water plant can be bid on - either Northampton or Blanford.

d.One and only one project can be selected from Projects 1, 5, and 7.

e.The Ludlow traffic safety plan can be bid on only if the Ludlow Bridge is bid on.

f.The Blanford water plant can be bid on only if either the Ludlow Bridge or Longmeadow municipal building project is bid on.

Project

Department

Expected Profit

(x 100,000)

Engineers needed

1. Northampton water plant.

Environmental

$8

3

2. Blanford water plant.

Environmental

$2

2

3. Springfield compost facility.

Environmental

$1

1

4. Ludlow Bridge

Structures

$6

5

5. Longmeadow municipal building

Structures

$5

4

6. Ludlow traffic safety plan

Transportation

$3

2

7. Williamstown bike trail.

Transportation

$1.2

1

Explanation / Answer

Since only one water plant can be bid on , lets first assume we choose (1)Northampton water plant ,

now we cant chose 5,7 accordingg to condition (d) and also can't chose (2) , and it is very necessary to choose atleast 1 out of 3 categories

therefore we can go for projects 1,4,6 -> satisfy all criteria

Similarily 2,4,6,7 satsify all criterias

another case would be 3,4,6,7

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