Matrices

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msjoharia

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Nov 29, 2011
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DQ: 1 If matrix A = [ 1 1.5 0.75]
[ 0.75 1 1.50 ] represents in thousands the number of Toyota, Honda, and Dodge vehicles sold in January and February by dealer one and matrix
B =[ 0.15 0.2 0.2]
[ 0.12 0.2 0.3] represents in thousands the numbers of Lexus, Lincoln, and Cadillac vehicles sold by dealer two during January and February, write down the matrix representing the total number of cars sold in January and February. Also, if the sale prices of a Toyota, Honda, Dodge, Lexus, Lincoln and Cadillac vehicle are $15,000, $16,000, $15,000, $35,000, $45,000, and $35,000, respectively, find which dealer had the higher revenue.


I am new to this area and is in need of how to set up the matrix and proceed for the solution. Please Assist If Able...
 
msjoharia said:
DQ: 1 If matrix A = [ 1 1.5 0.75]
[ 0.75 1 1.50 ] represents in thousands the number of Toyota, Honda, and Dodge vehicles sold in January and February by dealer one and matrix
B =[ 0.15 0.2 0.2]
[ 0.12 0.2 0.3] represents in thousands the numbers of Lexus, Lincoln, and Cadillac vehicles sold by dealer two during January and February, write down the matrix representing the total number of cars sold in January and February. Also, if the sale prices of a Toyota, Honda, Dodge, Lexus, Lincoln and Cadillac vehicle are $15,000, $16,000, $15,000, $35,000, $45,000, and $35,000, respectively, find which dealer had the higher revenue.


I am new to this area and is in need of how to set up the matrix and proceed for the solution. Please Assist If Able...
Click to expand...

\(\displaystyle A = \left( \begin{array}{ccc}
1 & 1.5 & 0.75 \\
0.75 & 1 & 1.50 \\ \end{array} \right)\)

\(\displaystyle B = \left( \begin{array}{ccc}
0.15 & 0.2 & 0.2 \\
0.12 & 0.2 & 0.3 \\ \end{array} \right)\)

To get the total number of cars sold in January, you need to add each of (1+1.5+0.75+0.15+0.2+0.2) for January and something similar for February. In the matrix, you will identify them like this:

\(\displaystyle \begin{array}{c|ccc}
& Toyota & Honda & Dodge \\ \hline
January & 1 & 1.5 & 0.75 \\
February & 0.75 & 1 & 1.50 \\ \end{array}\)

Your final matrix will be a 1 by 2 matrix.

===================

For the second part, you need to get the price of Toyota, Hondas, etc which means you multiply the number of cars sold by the price per car. This is done by the product of the matrices A and the price matrix which you will have to make:

\(\displaystyle Price = \left( \begin{array}{ccc}
1 & 1.5 & 0.75 \\
0.75 & 1 & 1.50 \\ \end{array} \right)
\left( \begin{array}{cc}
15 & 15\\
16 & 16 \\
15 & 15 \end{array} \right)\)

Here, the price are like this:

\(\displaystyle \begin{array}{c|cc}
& January & February\\ \hline
Toyota & 15 & 15\\
Honda & 16 & 16 \\
Dodge & 15 & 15\end{array}\)

When you get the result, you can add the two to get the total revenue for both January and February combined. You do the same for the other dealer.
 
Thank You!!

Are you available for tutoring if you are in the location of Royal Oak Mi


Unknown008 said:
\(\displaystyle A = \left( \begin{array}{ccc}
1 & 1.5 & 0.75 \\
0.75 & 1 & 1.50 \\ \end{array} \right)\)

\(\displaystyle B = \left( \begin{array}{ccc}
0.15 & 0.2 & 0.2 \\
0.12 & 0.2 & 0.3 \\ \end{array} \right)\)

To get the total number of cars sold in January, you need to add each of (1+1.5+0.75+0.15+0.2+0.2) for January and something similar for February. In the matrix, you will identify them like this:

\(\displaystyle \begin{array}{c|ccc}
& Toyota & Honda & Dodge \\ \hline
January & 1 & 1.5 & 0.75 \\
February & 0.75 & 1 & 1.50 \\ \end{array}\)

Your final matrix will be a 1 by 2 matrix.

===================

For the second part, you need to get the price of Toyota, Hondas, etc which means you multiply the number of cars sold by the price per car. This is done by the product of the matrices A and the price matrix which you will have to make:

\(\displaystyle Price = \left( \begin{array}{ccc}
1 & 1.5 & 0.75 \\
0.75 & 1 & 1.50 \\ \end{array} \right)
\left( \begin{array}{cc}
15 & 15\\
16 & 16 \\
15 & 15 \end{array} \right)\)

Here, the price are like this:

\(\displaystyle \begin{array}{c|cc}
& January & February\\ \hline
Toyota & 15 & 15\\
Honda & 16 & 16 \\
Dodge & 15 & 15\end{array}\)

When you get the result, you can add the two to get the total revenue for both January and February combined. You do the same for the other dealer.
Click to expand...
 
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