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A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints. Briefly describe what the objective function and each constraint represent. What type of integer optimization model is this?

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

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A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below.

Project	Time in first month	Time in second month	Time in third month	Revenue
A	6	8	6	22000
B	5	6	8	18000
C	8	7	6	16000
D	5	5	4	15000

Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue.

Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints. Briefly describe what the objective function and each constraint represent. What type of integer optimization model is this?

Note: Do NOT solve the problem after formulating.

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