The Left Coast Bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover, softcover, and plastic (for infants). The table shows the number of books in stock at the beginning of January. $\begin{array} { | l | l | l | l | }
\hline & \text { Hard } & \text { Soft } & \text { Plastic } \
\hline \text { San Francisco } & 1,000 & 2,000 & 5,000 \
\hline \text { Los Angeles } & 1,000 & 5,000 & 2,000 \
\hline
\end{array}$ Suppose its sales in January were as follows: 700 hardcover books, 1,300 softcover books, and 2,000 plastic books sold in San Francisco, and 400 hardcover, 300 softcover, and 500 plastic books sold in Los Angeles.
Now suppose that the stores maintained the same sales figures for the first 6 months of the year. Each month the chain restocked the stores from its warehouse by shipping 900 hardcover, 1,600 softcover, and 1,800 plastic books to San Francisco and 700 hardcover, 700 softcover, and 200 plastic books to Los Angeles.
Use matrix operations to determine the inventory in each store at the end of June.
A) $\left[ \begin{array} { c c c }
2,200 & 3,800 & 3,800 \
3,300 & 7,600 & 200
\end{array} \right]$
B) $\left[ \begin{array} { c c c }
2,200 & 3,700 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
C) $\left[ \begin{array} { c c c }
2,200 & 3,800 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
D) $\left[ \begin{array} { c c c }
2,300 & 3,700 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
E) $\left[ \begin{array} { c c c }
2,300 & 3,800 & 3,800 \
2,800 & 7,600 & 200
\end{array} \right]$

Question

The Left Coast Bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover, softcover, and plastic (for infants). The table shows the number of books in stock at the beginning of January. $\begin{array} { | l | l | l | l | } 
\hline & \text { Hard } & \text { Soft } & \text { Plastic } \
\hline \text { San Francisco } & 1,000 & 2,000 & 5,000 \
\hline \text { Los Angeles } & 1,000 & 5,000 & 2,000 \
\hline
\end{array}$   Suppose its sales in January were as follows: 700 hardcover books, 1,300 softcover books, and 2,000 plastic books sold in San Francisco, and 400 hardcover, 300 softcover, and 500 plastic books sold in Los Angeles.
Now suppose that the stores maintained the same sales figures for the first 6 months of the year. Each month the chain restocked the stores from its warehouse by shipping 900 hardcover, 1,600 softcover, and 1,800 plastic books to San Francisco and 700 hardcover, 700 softcover, and 200 plastic books to Los Angeles.
Use matrix operations to determine the inventory in each store at the end of June.
A) $\left[ \begin{array} { c c c } 
2,200 & 3,800 & 3,800 \
3,300 & 7,600 & 200
\end{array} \right]$
B) $\left[ \begin{array} { c c c } 
2,200 & 3,700 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
C) $\left[ \begin{array} { c c c } 
2,200 & 3,800 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
D) $\left[ \begin{array} { c c c } 
2,300 & 3,700 & 3,800 \
2,800 & 7,400 & 200
\end{array} \right]$
E) $\left[ \begin{array} { c c c } 
2,300 & 3,800 & 3,800 \
2,800 & 7,600 & 200
\end{array} \right]$

Quizplus · Accepted Answer

To find the inventory at the end of June, we calculate the net change in inventory each month (restock minus sales) and multiply by 6 (for 6 months), then add the result to the initial inventory. For San Francisco:- Hardcover: $900 - 700 = 200$ net restock per month, $200 \times 6 = 1200$ total, initial 1000, final $1000 + 1200 = 2200$.- Softcover: $1600 - 1300 = 300$ net restock per month, $300 \times 6 = 1800$ total, initial 2000, final $2000 + 1800 = 3800$.- Plastic: $1800 - 2000 = -200$ net decrease per month, $-200 \times 6 = -1200$ total, initial 5000, final $5000 - 1200 = 3800$.For Los Angeles:- Hardcover: $700 - 400 = 300$ net restock per month, $300 \times 6 = 1800$ total, initial 1000, final $1000 + 1800 = 2800$.- Softcover: $700 - 300 = 400$ net restock per month, $400 \times 6 = 2400$ total, initial 5000, final $5000 + 2400 = 7400$.- Plastic: $200 - 500 = -300$ net decrease per month, $-300 \times 6 = -1800$ total, initial 2000, final $2000 - 1800 = 200$.Thus, the correct inventory matrix at the end of June is:$\left[ \begin{array} { c c c } 2,200 & 3,800 & 3,800 \2,800 & 7,400 & 200\end{array} \right]$

The Left Coast Bookstore Chain Has Two Stores, One in San