10 Problem 7 10 Points Circle the correct answer in the foll

10 Problem 7: (10 Points) Circle the correct answer in the following five multiple choice questions: 1) If x, and x are binary variables where the value 1 signifies \"accept\" the project, the equation requiring the selection of(reonly if x, is first selected is: b. x, + x, 21 None of the above 2) A product, if it is manufactured at all, must be made in lot sizes s L. Let x be the quantity of the product produced. Which of the following constraints or sets constraints will be required? of b. x s Ly, where y 0 or 1: x20, y20 x Ly, where y 0 or 1i x20, y20 None of the above 3) If x, and r, are binary variables where the value 1 signifies \"accept\" the project, the equation requiring the selection of x if x, is selected and vice versa is x,2x If x, and x, are binary variables where the value 1 signifies \"accept\" the project, the equation requiring that if is selected, then x, cannot be selected, is 4) x, +x2 x, 2x d. 5) Ix, and * are binary variables where the value 1 signifies \"accept\" the project, the equation requiring that at least one of the pair, x, and x, will be selected is a. x,,21 d.

Solution

1. Given that both xj and xk are binary variables, then if xj is selected first, the chance that xk will be selected only if the sum of xj and xk are equal to 1(the acceptance criteria). Therefore it is option b.

2. The product should be manufactured less than or equal to L lot sizes and if x is manufactured then, x is either less than or equal to L and x is definitely greater than or equal to 0.Option a is correct.

3. Again look at the criteria , it should be option b.

4. Option should be that xj should be equal to xk. Option d is correct.

5. So for atleast one pair to be selected, option a is correct.