Microbucks Computers makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires 2 processor chips, 18 memory chips, and 20 vacuum tubes, and the Pom Classic requires 2 processor chips, 6 memory chips, and 50 vacuum tubes. At the beginning of the year, Microbucks has in stock 800 processor chips, 6,000 memory chips, and 13,000 vacuum tubes at the Pom II factory and 400 processor chips, 4,000 memory chips, and 40,000 vacuum tubes at the Pom Classic factory. It manufactures 50 Pom IIs and 50 Pom Classics each month.
Find the company's inventory of parts after 2 months, using matrix operations.

A) $\left[ \begin{array} { l l l }
600 & 4,200 & 11,000 \
200 & 3,400 & 35,000
\end{array} \right]$
B) $\left[ \begin{array} { l l l }
600 & 4,200 & 11,000 \
200 & 3,500 & 35,000
\end{array} \right]$
C) $\left[ \begin{array} { l l l }
600 & 4,200 & 11,000 \
400 & 3,400 & 35,000
\end{array} \right]$
D) $\left[ \begin{array} { l l l }
600 & 4,400 & 10,900 \
200 & 3,500 & 35,000
\end{array} \right]$
E) $\left[ \begin{array} { l l l }
700 & 4,200 & 11,000 \
200 & 3,400 & 34,900
\end{array} \right]$

Question

Microbucks Computers makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires 2 processor chips, 18 memory chips, and 20 vacuum tubes, and the Pom Classic requires 2 processor chips, 6 memory chips, and 50 vacuum tubes. At the beginning of the year, Microbucks has in stock 800 processor chips, 6,000 memory chips, and 13,000 vacuum tubes at the Pom II factory and 400 processor chips, 4,000 memory chips, and 40,000 vacuum tubes at the Pom Classic factory. It manufactures 50 Pom IIs and 50 Pom Classics each month.  
Find the company's inventory of parts after 2 months, using matrix operations.
 
A) $\left[ \begin{array} { l l l } 
600 & 4,200 & 11,000 \
200 & 3,400 & 35,000
\end{array} \right]$
B) $\left[ \begin{array} { l l l } 
600 & 4,200 & 11,000 \
200 & 3,500 & 35,000
\end{array} \right]$
C) $\left[ \begin{array} { l l l } 
600 & 4,200 & 11,000 \
400 & 3,400 & 35,000
\end{array} \right]$
D) $\left[ \begin{array} { l l l } 
600 & 4,400 & 10,900 \
200 & 3,500 & 35,000
\end{array} \right]$
E) $\left[ \begin{array} { l l l } 
700 & 4,200 & 11,000 \
200 & 3,400 & 34,900
\end{array} \right]$

Quizplus · Accepted Answer

The inventory after 2 months can be calculated by subtracting the parts used for production from the initial inventory. For 50 Pom IIs and 50 Pom Classics produced each month, in 2 months:- Processor chips used: $2 \times 50 \times 2 + 2 \times 50 \times 2 = 400$- Memory chips used for Pom II: $18 \times 50 \times 2 = 1,800$- Memory chips used for Pom Classic: $6 \times 50 \times 2 = 600$- Vacuum tubes used for Pom II: $20 \times 50 \times 2 = 2,000$- Vacuum tubes used for Pom Classic: $50 \times 50 \times 2 = 5,000$Subtracting these from the initial inventory gives:- Processor chips: $800 - 200 = 600$ at Pom II factory, $400 - 200 = 200$ at Pom Classic factory.- Memory chips: $6,000 - 1,800 = 4,200$ at Pom II factory, $4,000 - 600 = 3,400$ at Pom Classic factory.- Vacuum tubes: $13,000 - 2,000 = 11,000$ at Pom II factory, $40,000 - 5,000 = 35,000$ at Pom Classic factory.Thus, the correct inventory matrix after 2 months is:$\left[ \begin{array} { l l l } 600 & 4,200 & 11,000 \200 & 3,400 & 35,000\end{array} \right]$

Microbucks Computers Makes Two Computers, the Pomegranate II and the Pomegranate