SJC Engineering Corporation is considering undertaking several proposed projects

Question

SJC Engineering Corporation is considering undertaking several proposed projects for the next fiscal year. Let x_i = 1 if project i is selected and 0 if not; for i = 1, 2, 3, 4. Use the following equations to answer the questions. A) x_2 - x_3 lessthanorequalto 0 B) x_2 - x_3 greaterthanorequalto 0 C)x_2 - x_3 = 0 D) x_2 + x_3 lessthanorequalto 1 E) x_2 + x_3 greaterthanorequalto 1 F) x_2 + x_3 = 1 G) None of the above. Which equation satisfies the constraint such that "if project 2 is done, project 3 must not be done and vice versa"? Which equation satisfies the constraint such that "either project 2 or project 3 must be done, but not both"?

Explanation / Answer

Answer to the 1st question is option F since in that case if X2=1 then X3 has to be zero and vice versa.

Answer to the 2nd question is option D since in that case X2+X3 <= 1

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