Question

Let U be the 3 2 matrix [0.45 0.42, 0.25 0.35, 0.15 0.15]. 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 q1 be a vector in set of real numbers R2 that lists the output​ (measured in​ dollars) of products B and C manufactured during the first quarter of the​ year, and let q2, q3 ​, and q4 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 Upper Q = [q1 q2 q3 q4].A. The 4 columns of UQ list the profit made from selling products B and C during the 4 quarters of the year. B. The 3 rows of UQ list the costs for materials, labor, and overhead used to manufacture products B and C for the year. C. 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. D. The 4 columns of UQ list the total number of each product manufactured during the 4 quarters of the year.

Answer 1

C. 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.

Explanation:

`U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)`

`q_1` is a vector in the set of real numbers
`R^2` that lists the output​ (measured in​ dollars) of products B and C manufactured during the first quarter of the​ year.

Therefore:

Therefore, UQ has 4 columns and 3 rows.

The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.