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 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.

Assuming W1 and W2 are 0-1 integer variables indicating whether projects 1 and 2 are selected, respectively, the constraint W1 + W2 <= 1 means thatGroup of answer choicesthe projects are mutually exclusiveproject 1 is conditional on project 2project 2 is conditional on project 1none 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 is that the same decision be applied to project 2 and project 5. If project 2 is selected then project 5 is selected. And if project 2 is not selected then project 5 is not selected.  This condition is represented by the following constraint:

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?

A Corporation must decide between two mutually exclusive projects. Both projects requirean initial spending of $100 million, and they generate cash ows that are independent of thegrowth of the economy.Project A has equal probability of four gross payos: $80 million, $100 million, $120 million,or $140 million.Project B has a 50/50 chance of paying either $90 million or $130 million.Assuming that the shareholders are all risk-averse, prove that they unanimously prefer projectB to project A.1