In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraintneeds to be added to the formulation if one alternative must be chosen:A) x1 + x2 ≤ 1.B) x1 + x2 = 1.C) x1 − x2 ≤ 1.D) x1− x2 = 1.E) None of the choices is correct.

In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are twoprojects under consideration, A and B, and either both projects will be undertaken or noproject will be undertaken, then the following constraint needs to be added to theformulation:A) A ≤ B.B) A + B ≤ 2.C) A ≥ B.D) A = B.E) None of the choices is correct.

In a binary integer programming problem when a decision variable x = 1 corresponds to a “yes” decision and x = 0 to a “no” decision, which of the following formulates the condition that 3 alternatives (represented by decision variables x1, x2 and x3) are mutually exclusive?Group of answer choicesx1 + x2 + x3 >= 1x1 + x2 + x3 <= 2x1 + x2 + x3 = 1x1 + x2 + x3 <= 1

This is a modification of homework problem 14 in chapter 5.The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects. In the model for this problem Xi is a 0-1 variable for the selection of project i, where i = 1 to 8. One of the conditions in the modified model for this problem is that either project 2 or project 5 must be selected but not both of them. So, modify the constraint on decision variables x2 and x5 to represent this updated condition. Leave the other constraints (budget and personnel) the same. Then answer the following question.What is the value of the objective function at the updated solution?

Assuming W1, W2, and W3 are 0-1 integer variables, we have a constraint W1 + W2 + W3 ≤ 2 in the model. Which of the following statements is correct?Group of answer choicesminimum two variables can occur at the same time.all variables can be 0 at the same time.the variables are mutually exclusive.none of the above.

The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects. In the model for this problem Xi is a 0-1 variable for the selection of project i, where i = 1 to 8. One of the conditions in the model for this problem is that either project 2 or project 5 must be selected but not both of them. This condition is represented by the following constraint:Group of answer choices𝑥2≤𝑥5𝑥2+𝑥5=1𝑥2+𝑥5≤1𝑥2≥𝑥5