Let $U$ be the $32$ matrix $\left[\begin{array}{cc}0\mathrm{.}45& 0\mathrm{.}4\\ 0\mathrm{.}25& 0\mathrm{.}35\\ 0\mathrm{.}15& 0\mathrm{.}15\end{array}\right].$ The first column of $U$ lists the costs per dollar of output for manufacturing product $B,$ and the second column lists the costs per dollar of output for manufacturing product $C.$ The first row is the cost of materials, the second row is the cost of labor, and the third row is the cost of overhead. Let $q_1$ be a vector in $R^2$ that lists the output $($measured in dollars$)$ of products $B$ and $C$ manufactured during the first quarter of the year, and let $q_2,q_3,$ and $q_4$ be the analogous vectors that list the amounts of products $B$ and $C$ manufactured in the second, third, and fourth quarters, respectively. Give an economic desciption of the data in the matrix $UQ,$ where $Q=\left[\begin{array}{cccc}{q}_1& q_2& q_3& q_4\end{array}\right],$

Choose the correct answer below.

A$.$ The $3$ rows of UQ list the costs for materials, labor, and overhead used to manufacture products $B$ and $C$ for the year.

B$.$ The $4$ columns of UQ list the total costs for materials, labor, and overhead used to manufacture products $B$ and $C$ during the $4$ quarters of the year.

C$.$ The $4$ columns of UQ list the total number of each product manufactured during the $4$ quarters of the year.

D$.$ The $4$ columns of UQ list the profit made from selling products $B$ and $C$ during the $4$ quarters of the year.