A paper mill has received an order for rolls of paper. The customer wants 400 rolls that are 12" wide, 300 rolls that are 18" wide and and 200 rolls that are 24" wide. The company has 40" wide rolls of paper which can be cut to the appropriate width. The company has four cutting patterns. Pattern A will cut (from one 40" wide roll) three rolls of 12". Pattern B will cut one roll of 12" and one roll of 18". Pattern C will cut one roll of 12" and one roll of 24". Pattern D will cut two rolls of 18". What is the number of 40" wide rolls the company must use to fill the order, without producing more than what the customer is asking?

Refer to the Paper Cutting Problem. Start with the original information. The customer increases his demand for 12" rolls from 400 to 450. In this case:

	A.	The number of rolls used for cutting pattern B is zero
	B.	The total number of rolls used is 434
	C.	Both A and B
	D.	Neither A nor B

Refer to the Paper Cutting Problem. Start with the original information. A new requirement is added such that the number of rolls in each pattern should be greater than 30. Then which of the following statements is true?

	A.	The total number of rolls used is greater than 410
	B.	The number of rolls in cutting pattern B is 80
	C.	Both A and B.
	D.	Neither A nor B.

Refer to the Paper Cutting Problem. Start with the original information. A new requirement is added such that the number of rolls in each pattern should be greater than 50, and that production can exceed customer demand. In this case, which of the following statements is true?

	A.	Cutting pattern D uses more rolls than Cutting Pattern A and Cutting Pattern B combined.
	B.	Cutting pattern C uses more rolls than all other patterns combined.
	C.	Both A and B.
	D.	Neither A nor B.

Refer to the Paper Cutting Problem. Start with the original information. At the optimal solution, to minimize the number of rolls while meeting all the constraints, how many rolls are used in Cutting Pattern B?

	A.	1
	B.	2
	C.	7
	D.	11

Refer to the Paper Cutting Problem. Start with the original information. At the optimal solution, the company needs more rolls in Cutting Pattern C than Cutting Pattern D.

	A.	This is true
	B.	This is false