Canning Tomato Products. Jaeger Foods produces tomato sauce and tomato paste, ca

shadsiei

shadsiei

Answered question

2021-09-25

Canning Tomato Products. Jaeger Foods produces tomato sauce and tomato paste, canned in small, medium, large, and giant-sized cans. The matrix A gives the size (in ounces) of each container.
SmallMediumLargeGiantOunces6101428=A
The matrix B tabulates one day's production of tomato sauce and tomato paste.
Cans of sauceCans of pasteSmall20002500Medium30001500Large25001000Giant1000500=B
a) Calculate the product AB.
b) Interpret the entries in the product matrix AB.

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-09-26Added 117 answers

Step 1
Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
And by using the product of the matrix 4×1 and 2×4 will result the matrix of 2×1.
AB=[6101428]×AB=[2000250030001500250010001000500]
Step 2
Now multiply the row of the A matrix with the first column of the matrix B and keep on adding the multiples then multiply the row of the A matrix with the second column of the matrix B and keep on adding the multiples.
AB=[6101428]×AB=[2000250030001500250010001000500]
=[(6×2000)+(10×3000)+(14×2500)+(28×1000)(6×2500)+(10×1500)+(14×1000)+(28×500)]
=[12000+30000+35000+2800015000+15000+14000+14000]
=[10500058000]

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