One serving of Post Shredded Wheat® supplies 160 calories, 5 g of protein, 6 g of fiber, and 1 g of fat. One serving of Crispix® supplies 110 calories, 2 g of protein, .1 g of fiber, and .4 g of fat. a. Set up a matrix B and a vector u such that Bu gives the amounts of calories, protein, fiber, and fat contained in a mixture of three servings of Shredded Wheat and two servings of Crispix. b. [M] Suppose that you want a cereal with more fiber than Crispix but fewer calories than Shredded Wheat. Is it possible for a mixture of the two cereals to supply 130 calories, 3.20 g of protein, 2.46 g of fiber, and .64 g of fat? If so, what is the mixture?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
Question
One serving of Post Shredded Wheat® supplies 160 calories,
5 g of protein, 6 g of fiber, and 1 g of fat. One serving of
Crispix® supplies 110 calories, 2 g of protein, .1 g of fiber,
and .4 g of fat.
a. Set up a matrix B and a vector u such that Bu gives the
amounts of calories, protein, fiber, and fat contained in
a mixture of three servings of Shredded Wheat and two
servings of Crispix.
b. [M] Suppose that you want a cereal with more fiber than
Crispix but fewer calories than Shredded Wheat. Is it
possible for a mixture of the two cereals to supply 130
calories, 3.20 g of protein, 2.46 g of fiber, and .64 g of
fat? If so, what is the mixture?
Transcribed Image Text:One serving of Post Shredded Wheat® supplies 160 calories, 5 g of protein, 6 g of fiber, and 1 g of fat. One serving of Crispix® supplies 110 calories, 2 g of protein, .1 g of fiber, and .4 g of fat. a. Set up a matrix B and a vector u such that Bu gives the amounts of calories, protein, fiber, and fat contained in a mixture of three servings of Shredded Wheat and two servings of Crispix. b. [M] Suppose that you want a cereal with more fiber than Crispix but fewer calories than Shredded Wheat. Is it possible for a mixture of the two cereals to supply 130 calories, 3.20 g of protein, 2.46 g of fiber, and .64 g of fat? If so, what is the mixture?
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