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.
Formulate a binary linear programming problem to select the mix of projects that will result in the maximum profits for the firm.