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.

Practical Management Science
6th Edition
ISBN:9781337406659
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Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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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