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# Developing and Implementing a LP Model

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A university needs to put together a committee to handle students' complaints. To ensure that all perspectives are represented, it is necessary to have a diverse committee by including at least one female, one male, one student, one administrator and one faculty member. Ten individuals have been nominated but since it is important to maintain the anonymity of the committee, the individuals are identified by the letters A to J. The mix of individuals in the different categories is given as follows:

Category Individual
Females A, B, C, D, E
Males F, G, H, I, J
Students A, B, C, J
Faculty D, G,H, I

The university wants to form the smallest committee possible with representation from each of the five categories.

a) Formulate a linear mathematical model to find the optimal solution and put it in standard format. Clearly define your decisions variables, objective function and constraints

b) Implement your model in Excel and use Solver to find the optimal solution. Include a snapshot of your answer in the report

c) If individuals (A) and (F) do not get along, and therefore, we cannot have them together on the committee, what would be the new linear constraint that can model this condition? Just include the constraint without repeating the whole formulation and remember that the model must remain linear (i.e., no IF-THEN or similar functions are allowed). Implement this additional condition in Excel and provide the new solution.

d) Suppose that in addition to the condition in part (c), faculty member (I) may have to decline joining the committee due to a project commitment, in which case student (A) must also decline to be on the project with her professor. What would be the new linear constraint that can model this condition? Just include the constraint without repeating the whole formulation and remember that the model must remain linear (i.e., no IF-THEN or similar functions are allowed). Implement this additional condition in Excel and provide the new solution.

https://brainmass.com/math/discrete-math/developing-implementing-lp-model-513215

#### Solution Preview

a) Formulate a linear mathematical model to find the optimal solution and put it in standard format. Clearly define your decisions variables, objective function and constraints
Decision Variable:
XA - A binary variable which takes a value of 1 if individual A is selected in the committee, else it takes a value of 0
XB - A binary variable which takes a value of 1 if individual B is selected in the committee, else it takes a value of 0
XC - A binary variable which takes a value of 1 if individual C is selected in the committee, else it takes a value of 0
XD - A binary variable which takes a value of 1 if individual D is selected in the committee, else it takes a value of 0
XE - A binary variable which takes a value of 1 if individual E is selected in the committee, else it takes a value of 0
XF - A binary variable which takes a value of 1 if individual F is selected in the committee, else it takes a value of 0
XG - A binary variable which takes a value of 1 if individual G is selected in the ...

#### Solution Summary

Solution builds a linear programming model and solves it by using Solver in MS Excel to get the optimal solution. All needed reports and screen shots are attached in MS Excel for the better clarity of solution.

\$2.19

## Operations Research

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.

(see chart in attached file)

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.

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