Math Problem Statement
Solution
To determine how many pounds of wheat, oats, and raisins are needed for the order using matrix multiplication, we can represent the problem as a matrix equation.
We have the following information from the image:
The proportion matrix for the cereals and their ingredient proportions (wheat, oats, raisins) is:
0.75 & 0.25 & 0 \\ 0.50 & 0.25 & 0.25 \\ 0.25 & 0.50 & 0.25 \end{bmatrix}$$ The order matrix $$B$$ for the pounds of each type of cereal is: $$B = \begin{bmatrix} 1300 \\ 1820 \\ 2080 \end{bmatrix}$$ We need to calculate how many pounds of wheat, oats, and raisins are required. This can be done using matrix multiplication: $$X = A \times B$$ Where $$X$$ represents the pounds of wheat, oats, and raisins. Let me calculate this for you.The result of the matrix multiplication shows that the Health Fare Cereal Company will need the following amounts of ingredients to fill the order: - **1430 pounds of wheat** - **1625 pounds of oats** - **1755 pounds of raisins** Would you like further details on the matrix operations,Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Proportions
Formulas
Matrix Multiplication (AX = B)
Theorems
Linear Combination of Ingredients
Suitable Grade Level
Grades 10-12
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