Question

Let x1, x2, and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?a.x1+ x2+ x3>2b.x1+ x2+ x3<2c.x1+ x2+ x3= 2d.x1- x2= 0

Answer 1

Answer:

Correct statement: a. x₁ + x₂ + x₃ > 2

Step-by-step explanation:

The variables x₁, x₂ and x₃ takes value 0 if the projects are not done and 1 if the projects are done.

Consider that at least two projects are done, i.e. 2 or more projects are done.

This can happen in:

x₁ = 0, x₂ = 1 and x₃ = 1

x₁ = 1, x₂ = 0 and x₃ = 1

x₁ = 1, x₂ = 1 and x₃ = 0

x₁ = 1, x₂ = 1 and x₃ = 1

The statement (x₁ + x₂ + x₃ > 2) will be true only when all the variables takes the value 1.

This statement implies that 2 projects are definitely done.

Thus, the correct statement is (a).