Infocomp Systems Lab is a research and development (R&D)company that develops computer systems and software primarily forthe medical industry. The lab has proposals from its ownresearchers for eight new projects. Each of the proposed researchprojects requires limited resources, and it is not possible toundertake all of them. The following table shows the developmentalbudget, the number of researchers, and the expected annual salesfrom each project if successfully developed and implemented:

Project	Developmental Budget ($1,000,000s)	Number of Research Personnel	Expected Annual Sales ($1,000,0005)
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 lab has developed the following set of prioritized goals forselecting which projects to initiate:

(1) The company would like to remain within a totaldevelopmental budget of $5,000,000.

(2) The number of available research personnel is 27, andInfocomp would like to avoid obtaining extra researchers.

(3) The company would like the expected future annual sales fromthe implemented projects to be at least $6,500,000.

(4) Projects 1, 3, 4, and 6 are considered offensive in thatthey represent new product initiatives, while projects 2, 5, 7, and8 are existing product upgrades and thus defensive in nature. Thelab would like to select at least two projects from each group.

(5) Projects 2, 3, 5, 6, and 7 are considered the most risky ofthe projects, and the company would prefer not to select any morethan three of these projects.

(6) The lab’s owner has indicated that she would like to seeprojects 5 and 6 initiated if doing so would not interfere with theachievement of any of the more important goals determined by thelab’s top management.

a. Formulate a goal programming model to determine whichprojects Infocomp Systems Lab should select to best achieve itsgoals.

No need to solve in excel. Looking for Decision variables,objective function and constraints.