Convert the data to a matrix and find the inventory for 2014.

Computer inventory in fall 2013:

[latex]{C}_{2013}=\left[\begin{array}{c}15\\ 16\\ 16\end{array}\begin{array}{c}27\\ 34\\ 34\end{array}\right][/latex]

To calculate how much computer equipment will be needed in 2014, we multiply all entries in matrix [latex]C[/latex] by [latex]0.15[/latex].

[latex]\left(0.15\right){C}_{2013}=\left[\begin{array}{c}\left(0.15\right)15\\ \left(0.15\right)16\\ \left(0.15\right)16\end{array}\begin{array}{c}\left(0.15\right)27\\ \left(0.15\right)34\\ \left(0.15\right)34\end{array}\right]=\left[\begin{array}{c}2.25\\ 2.4\\ 2.4\end{array}\begin{array}{c}4.05\\ 5.1\\ 5.1\end{array}\right][/latex]

We must round up to the next integer, so the amount of new equipment needed is

[latex]\left[\begin{array}{c}3\\ 3\\ 3\end{array}\begin{array}{c}5\\ 6\\ 6\end{array}\right][/latex]

Adding the two matrices as shown below, we see the new inventory amounts.

[latex]\left[\begin{array}{c}15\\ 16\\ 16\end{array}\begin{array}{c}27\\ 34\\ 34\end{array}\right]+\left[\begin{array}{c}3\\ 3\\ 3\end{array}\begin{array}{c}5\\ 6\\ 6\end{array}\right]=\left[\begin{array}{c}18\\ 19\\ 19\end{array}\begin{array}{c}32\\ 40\\ 40\end{array}\right][/latex]

This means

[latex]{C}_{2014}=\left[\begin{array}{c}18\\ 19\\ 19\end{array}\begin{array}{c}32\\ 40\\ 40\end{array}\right][/latex]

Thus, Lab A will have [latex]18[/latex] computers, [latex]19[/latex] computer tables, and [latex]19[/latex] chairs; Lab B will have [latex]32[/latex] computers, [latex]40[/latex] computer tables, and [latex]40[/latex] chairs.

We are also given the prices of the equipment, as shown in the table below.

How can we find the total cost for the equipment needed for each team?