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

Answer:

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.

Step-by-step 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:

$UQ=\left\begin{array}{ccc}\\ Cost of Materials\\ Cost of Labour\\ Cost of Overhead\end{array}\right\left(\begin{array}{cc} Product B& Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)$

$=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)$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.