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.