Assignment:
Infocomp Systems is a research and development laboratory firm that develops computer systems and software primarily for the medical industry. The laboratory has proposals from its own researchers for eight new projects. Each of the proposed research projects requires limited resources and it is not possible to undertake all of them. The following table reflects the development budget, the number of researchers, and the expected annual sales from each project if successfully developed and implemented.
|
Project
|
Developmental Budget
($ millions)
|
Number of Research Personnel
|
Expected Annual Sales ($ millions)
|
|
1
|
$0.675
|
6
|
$0.82
|
|
2
|
1.050
|
5
|
1.75
|
|
3
|
0.725
|
7
|
1.60
|
|
4
|
0.430
|
8
|
1.90
|
|
5
|
1.240
|
10
|
0.93
|
|
6
|
0.890
|
6
|
1.70
|
|
7
|
1.620
|
7
|
1.30
|
|
8
|
1.200
|
6
|
1.80
|
The firm has developed the following set of prioritized goals for selecting projects to initiate:
• The company wants to remain within a total development budget of $5,000,000.
• The company wants to avoid hiring additional research personnel beyond the current staff level of 27 researchers.
• The company would like the expected future annual sales from the implemented projects to be at least $6,500,000.
• Projects 1, 3, 4, and 6 are considered strategically offensive in that they represent new product initiatives, while 2, 5, 7, and 8 are existing product upgrades and therefore defensive in nature. The company would like to select at least two products from each group.
• Projects 2, 3, 5, 6, and 7 are considered the most risky of the projects, and the company would prefer not to select more than three from this group.
• The president of Infocomp Systems has expressed an interest in the initiation of projects 5 and 6 unless these selections are in conflict with other goals.
a. Formulate a linear goal programming model to determine the projects to select that will best achieve the company’s goals.
b. Determine the solution that will best achieve the company’s goals in project selection, including the projects selected and the levels of goal achievement.
Provide complete and step by step solution for the question and show calculations and use formulas.