1 to 4 are based on this problem. Jack is considering purchase the following items for his backpacking trip. The cost and the condition of each item are listed in the following table: Item Number Description Condition 1 Backpacking Tarp Not if 3 and only if 2 2 Hammock Not if 3 3 Backpacking Tent Not if 1 or 2 4 Sleeping Bag Must if 5 5 Sleeping Pad Only if 4 Ci is the Cost of item i. Jack needs at least 3 items. Formulate an IP to minimize the total cost. Decision Variables: Xi=1 if item i is purchased; 0 otherwise. Question 1: What are the constraints for item 1? a.) X1+X3<=1; X2-X1<=0 b.) X1-X2-X3<=-1 c.) X1+X3<=1; X1-X2<=0 d.) X1+X3>=1; X1-X2<=0 Question 2: What is the constraint for item 2? a.) X2-X3<=0 b.) X2+X3<=1 c.) X2+X3>=1 d.) X2+X3<=0 Question 3: What is the constraint for item 4? a.) X4+X5>=0 b.) X4-X5>=0 c.) X4-X5<=0 d.) X4+X5<=0 Question 4: Which statement about the formulation is not true? a.) In this problem, the non-negativity constraint is not required. b.) We should declare Xi binary variable. c.) X1+X2+X3+X4+X5<=3 ensure Jack purchase at least 3 items. d.)The constraint for item 5 is X5-X4<=0.
1 to 4 are based on this problem.
Jack is considering purchase the following items for his backpacking trip. The cost and the condition of each item are listed in the following table:
| Item Number | Description | Condition |
| 1 | Backpacking Tarp | Not if 3 and only if 2 |
| 2 | Hammock |
Not if 3 |
| 3 | Backpacking Tent | Not if 1 or 2 |
| 4 | Sleeping Bag | Must if 5 |
| 5 | Sleeping Pad | Only if 4 |
Ci is the Cost of item i. Jack needs at least 3 items. Formulate an IP to minimize the total cost.
Decision Variables:
Xi=1 if item i is purchased; 0 otherwise.
Question 1:
What are the constraints for item 1?
a.) X1+X3<=1; X2-X1<=0
b.) X1-X2-X3<=-1
c.) X1+X3<=1; X1-X2<=0
d.) X1+X3>=1; X1-X2<=0
Question 2:
What is the constraint for item 2?
a.) X2-X3<=0
b.) X2+X3<=1
c.) X2+X3>=1
d.) X2+X3<=0
Question 3:
What is the constraint for item 4?
a.) X4+X5>=0
b.) X4-X5>=0
c.) X4-X5<=0
d.) X4+X5<=0
Question 4:
Which statement about the formulation is not true?
a.) In this problem, the non-negativity constraint is not required.
b.) We should declare Xi binary variable.
c.) X1+X2+X3+X4+X5<=3 ensure Jack purchase at least 3 items.
d.)The constraint for item 5 is X5-X4<=0.
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