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On certain day stainless steel containers were manufactured 500 with 10-gallon (gal) capacity, 350 with 5-gal capacity, and 400 with 1-gal capacity

On the same day aluminum containers were manufactured: 700 with 10-gal capacity, 500 with 5-gal capacity, and 850 with 1-gal capacity.

The table represents the given data

A 2 by 3 matrix formed from this data will be $\left[\begin{array}{ccc}500& 350& 400\\ 700& 500& 850\end{array}\right]$

A 3 by 2 matrix representing the same data will be$\left[\begin{array}{cc}500& 700\\ 350& 500\\ 400& 850\end{array}\right]$

The table represents the amount of material used for each container

A 3 by 1 matrix formed from this data will be$\left[\begin{array}{c}15\\ 8\\ 3\end{array}\right]$

For finding the day's ge of materials,multiplay the two matrices $\left[\begin{array}{c}15\\ 8\\ 3\end{array}\right]and\left[\begin{array}{ccc}500& 350& 400\\ 700& 500& 850\end{array}\right]$

$$\begin{gathered} \left[\begin{array}{ccc}500& 350& 400\\ 700& 500& 850\end{array}\right]\left[\begin{array}{c}15\\ 8\\ 3\end{array}\right]=\left[\begin{array}{c}500x15+350x8+400x3\\ 700x15+500x8+850x3\end{array}\right] \\ 2x33x12x1 \\ =\left[\begin{array}{c}11,500\\ 17,050\end{array}\right] \end{gathered}$$

The 1 by 2 matrix representing the cost per pound for the material used is$\left[\begin{array}{cc}0.10& 0.05\end{array}\right]$

The table represents the cost per pound for the material used

The 1 by 2 matrix representing the cost per pound for the material used is$\left[\begin{array}{cc}0.10& 0.05\end{array}\right]$

For finding the total cost of the day's production,multiplay the matrices $\left[\begin{array}{c}11500\\ 17050\end{array}\right]and\left[\begin{array}{cc}0.10& 0.05\end{array}\right]$

$$\begin{gathered} \left[\begin{array}{c}11500\\ 17050\end{array}\right]\left[\begin{array}{cc}0.10& 0.05\end{array}\right]=11500(0.10)+17050(0.05) \\ =1150+852.5 \\ =2002.5 \end{gathered}$$

Therefore,the total cost of the day's production is$\$2002.5$