Question

A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.​

Answer 1

Using matrix algebra, the material cost of making one of each product at each location is as follows:​

                       Product X    Product Z

Location A        birr 38          birr 50

Location B        birr 38          birr 49.5

What is matrix algebra?

Matrix algebra involves the arrangement of numbers in a rectangular array.

Matrices are arranged in columns and rows to express some mathematical values.

Data and Calculations:

Matrix O: Materials Requirement Per Unit

                      Steel    Glass    Plastic

Product X         3            1             2

Product Z         4          0.5           3

Matrix P: Materials Cost Per Unit

                      Steel    Glass    Plastic

Location A      10           2           3

Location B       9           3           4

Matrix R: (O x P) Material Cost of Product X

                      Steel    Glass    Plastic   Total

Location A     30           2           6          38

Location B     27           3           8          38

Matrix R: (O x P) Material Cost of Product Z

                      Steel    Glass    Plastic   Total

Location A     40          1             9          50

Location B     36          1.5         12         49.5

Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.

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