### Constraining Project Selection in Linear Programming**Scenario:**- Project 3 **can be selected only if both** Projects 1 and 2 are selected.- However, if both Projects 1 and 2 are selected, Project 3 **does not necessarily have to be selected**.**Question:**What is the appropriate constraint for this scenario?**Options:**1. $ x_3 \geq x_1 + x_2 $2. $ x_1 + x_2 \geq x_3 $3. $ x_1 \geq x_3 $ and $ x_2 \geq x_3 $4. $ x_1 + x_2 + x_3 = 2 $5. None of the above**Explanation:**Each option represents a potential constraint in a linear programming model to ensure the projects are selected based on the defined conditions. It is key in understanding how to formulate constraints that express the logical conditions given.### Detailed Analysis of Options:1. **$ x_3 \geq x_1 + x_2 $**: This option implies that Project 3 can only be selected if the combined selection values of Projects 1 and 2 exceed or match Project 3’s value. This is incorrect because it does not ensure both Projects 1 and 2 must be selected before Project 3 is considered.2. **$ x_1 + x_2 \geq x_3 $**: This implies that the selection of Project 3 can only occur if Projects 1 and 2 together meet or exceed the value of Project 3. This does not impeccably capture the requirement.3. **$ x_1 \geq x_3 $ and $ x_2 \geq x_3 $**: This suggests that Projects 1 and 2 each need to be at least as large as Project 3, individually. This is a more complex condition but still not entirely correct as it doesn't assure the required combination.4. **$ x_1 + x_2 + x_3 = 2 $**: This equality constraint is not appropriate as it specifically constrains the combined values of Projects 1, 2, and 3 to be 2, which is restrictive and incorrect for the problem’s requirements.5. **None of the above**:

Project 3 can be selected only if both Projects 1 and 2 are selected, but if both Projects 1 and 2 are selected, Project 3 doesn't have to be selected. The appropriate constraint would be x3>=x1+x2 x1+x2>=x3 O x1>=x3 and x2>=x3 x1+x2+x3<=2 None of the above

Project 3 can be selected only if both Projects 1 and 2 are selected, but if both Projects 1 and 2 are selected, Project 3 doesn't have to be selected. The appropriate constraint would be x3>=x1+x2 x1+x2>=x3 O x1>=x3 and x2>=x3 x1+x2+x3<=2 None of the above

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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