INVENTORY A company sells five models of computers through...

INVENTORY A company sells five models of computers through three retail outlets. The inventories are represented by $S$. \begin{equation} \stackrel{\mbox{Model}}{ \overbrace{ \begin{array}{@{}r@{\quad}ccrr@{}} A & B & C & D & E \\ \end{array}}} \end{equation} \begin{equation} \left. S=\left[\begin{array}{@{}r@{\quad}ccrr@{}} 3 & 2 & 2 & 3 & 0 \\ 0 & 2 & 3 & 4 & 3 \\ 4 & 2 & 1 & 3 & 2 \end{array}\right] \begin{array}{r} 1 \\ 2 \\ 3 \end{array}\right\} \textrm{Outlet} \end{equation} The wholesale and retail prices are represented by $T$. \begin{equation} \stackrel{\mbox{Price}}{ \overbrace{ \begin{array}{@{}r@{\quad}ccrr@{}} \textrm{Wholesale} & \textrm{Retail} \\ \end{array}}} \end{equation} \begin{equation} \left. T=\left[\begin{array}{@{}r@{\quad}ccrr@{}} \$840 & \$1100 \\ \$1200 & \$1350 \\ \$1450 & \$1650 \\ \$2650 & \$3000 \\ \$3050 & \$3200 \\ \end{array}\right] \begin{array}{r} A \\ B \\ C \\ D \\ E \end{array}\right\} \textrm{Outlet} \end{equation}

INVENTORY A company sells five models of computers through three retail outlets. The inventories are represented by $S$.

\begin{equation}
\stackrel{\mbox{Model}}{
\overbrace{
\begin{array}{@{}r@{\quad}ccrr@{}}
A & B & C & D & E \\
\end{array}}}
\end{equation}

\begin{equation}
\left.
S=\left[\begin{array}{@{}r@{\quad}ccrr@{}}
3 & 2 & 2 & 3 & 0 \\
0 & 2 & 3 & 4 & 3 \\
4 & 2 & 1 & 3 & 2
\end{array}\right] \begin{array}{r} 1 \\ 2 \\ 3 \end{array}\right\} \textrm{Outlet}
\end{equation}

The wholesale and retail prices are represented by $T$.

\begin{equation}
\stackrel{\mbox{Price}}{
\overbrace{
\begin{array}{@{}r@{\quad}ccrr@{}}
\textrm{Wholesale} & \textrm{Retail} \\
\end{array}}}
\end{equation}

\begin{equation}
\left.
T=\left[\begin{array}{@{}r@{\quad}ccrr@{}}
\$840 & \$1100 \\
\$1200 & \$1350 \\
\$1450 & \$1650 \\
\$2650 & \$3000 \\
\$3050 & \$3200 \\
\end{array}\right] \begin{array}{r} A \\ B \\ C \\ D \\ E \end{array}\right\} \textrm{Outlet}
\end{equation}

Transcript

00:01 Now we are in this question we've been given two mattresses.

00:04 It is already specified in the question.

00:07 The mattress is having the elements 3 -2 -2 -30, then 0 -2 -3 -4 -3.

00:17 And the last one -three -three -two.

00:18 Okay, this is the mattress is.

00:22 As i said, it is already given in the question itself.

00:27 And the other mattress t is having the elements 840.

00:31 Just writing down the elements i'm not writing that dollar sign over here 1200 then 1 350 then 1450 1650 2650 then 3 000 and the last way is having the element 3 05050 30200 like this okay so these are the two mattresses okay we just have to determine the mattresses that is we have to multiply these two matrices so for that let's find out the order of both the matrices first the mattresses is having three rows and five columns that means it is a three by five ordered matrix and the matrix t is having five rows and two columns that means five by two order matrix so it is clear that the mattress st is possible and it will be of the order three by two now the question arises how do we multiply two matrices.

01:35 So for that we just take up the dot product of the rules of the first matrix and the columns of the second matrix.

01:42 So what you'll do simply three times 840 plus 2 times 1200 plus 2 times 141 ,450 plus 3 times 2 ,650 and plus 0.

01:56 So that will give you 15 ,770.

02:03 This but similarly for the other element again what i'm going to do is now see this will be a three by two quadroth matrix no so two column the other column will have the element that will be obtained by multiplying three times eleven hundred how i'm just taking up the first row of the first matrix and the second column of the second matrix so three times eleven hundred plus two times one thousand three hundred and fifty plus two times one thousand six and fifty plus three times 3 ,000 plus 0.

02:34 So that will be 18 ,300...

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