A small company manufactures a touring bike (T), a mountain bike (M), and a racing bike (R). The touring bike retails at $1000, the mountain bike retails at $700, and the racing bike retails at $1,500. The company has two warehouses, one in Adelaide and one in Mount Gambier. The Adelaide warehouse has a stock of 10 T, 15 M, and 20 R. The Mount Gambier warehouse has a stock of 5 T, 15 M, and 10 R. (a) Summarise the stock in a matrix W of order 2 × 3 preserving the order T, M, R for the columns, and with Adelaide corresponding to the first row. (b) Let S represent the total number of bikes of each type that the company has in stock. Then S = AW for some matrix A. Write down what the matrix A must be. (c) Use matrix multiplication to calculate S.
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A small company manufactures a touring bike (T), a mountain bike (M), and a racing bike (R). The touring bike retails at $1000, the mountain bike retails at $700, and the racing bike retails at $1,500. The company has two warehouses, one in Adelaide and one in Mount Gambier. The Adelaide warehouse has a stock of 10 T, 15 M, and 20 R. The Mount Gambier warehouse has a stock of 5 T, 15 M, and 10 R.
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(a) Summarise the stock in a matrix W of order 2 × 3 preserving the order T, M, R for the columns, and with Adelaide corresponding to the first row.
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(b) Let S represent the total number of bikes of each type that the company has in stock. Then S = AW for some matrix A. Write down what the matrix A must be.
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(c) Use matrix multiplication to calculate S.
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(d) Write down a
vector B such that a matrix product with W willgive the retail value of stock V in each warehouse.
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(e) Use your answer to (d) and matrix multiplication to calculate the
retail value of stock V in each warehouse.
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(f) Use your answers above to write down the formula for a matrix product that gives the total value of all stock Z, and calculate this value using matrix multiplication.
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