Second consulting is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and support personnel required for each project, and the expected profits for each project are summarized in the following table: ​ ​ Project ​ 1 2 3 4 5 6 Engineers required 20 55 47 38 90 63 Support personnel required 15 45 50 40 70 70 Profit ($1,000,000s) 1.0 1.8 2.0 1.5 3.6 2.2   There are 175 engineers available and 150 support personnel available for these projects. Further, no more than 3 projects can be done. Formulate an integer program to solve this problem. Define the decision variables needed to model this problem. The objective is to maximize profit. Give the objection function. Write the constraints. What is the final answer? Explain in detail.

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Second consulting is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and support personnel required for each project, and the expected profits for each project are summarized in the following table:

Project

1

2

3

4

5

6

Engineers required

20

55

47

38

90

63

Support personnel required

15

45

50

40

70

70

Profit ($1,000,000s)

1.0

1.8

2.0

1.5

3.6

2.2

 

There are 175 engineers available and 150 support personnel available for these projects. Further, no more than 3 projects can be done. Formulate an integer program to solve this problem.

  1. Define the decision variables needed to model this problem.
  2. The objective is to maximize profit. Give the objection function.
  3. Write the constraints.
  4. What is the final answer? Explain in detail.
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