The Seedy Vin Company produces Riesling, Charbono, and Ros wines. There are three procedures for producing each

The Seedy Vin Company produces Riesling, Charbono, and Rosé wines. There are three procedures for producing each wine (the procedures for production affect the cost of the final product). One procedure allows an outside company to bottle the wine; a second allows the wine to be produced and bottled at the winery; a third allows the wine to be estate bottled. The amount of wine produced by the Seedy Vin Company by each method is shown by the matrix

\[\begin{aligned}
& \text { Riesling } \\
& {[\mathrm{W}]=\left[\begin{array}{lll}
2 & \text { Charbono } & \text { Rosé } \\
4 & 1 & 3 \\
1 & 2 & 6
\end{array}ight] \text { outside bottling }} \\
&
\end{aligned}\]

Suppose the cost for each method of production is given by the matrix

\[\begin{aligned}
& {[\mathrm{C}]=\left[\begin{array}{lll}
\text { outside } & \text { winery estate }]
\end{array}ight.} \\
& =\left[\begin{array}{lll}
1 & 4 & 6
\end{array}ight]
\end{aligned}\]

Suppose the production cost of a unit of each type of wine is given by the matrix

\[[D]=\left[\begin{array}{l}
40 \\
60 \\
30
\end{array}ight] \begin{aligned}
& \text { Riesling } \\
& \text { Charbono } \\
& \text { Rosé }
\end{aligned}\]

a. Find the cost of producing each of the three types of wine.

b. Find the total cost for producing each unit of the different types of wine for these methods of production.

c. Find \(([\mathrm{C}][\mathrm{W}])[\mathrm{D}]\) and \([\mathrm{C}]([\mathrm{W}][\mathrm{D}])\). Give a verbal interpretation for these products.