1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Liula [17]
3 years ago
12

A certain 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). At the beginning of January, the central computer showed the following books in stock.
Hard Soft Plastic
San Francisco 1,000 3,000 6,000
Los Angeles 1,000 6,000 3,000
Its sales in January were as follows: 600 hardcover books, 1,300 softcover books, and 2,000 plastic books sold in San Francisco, and 400 hardcover, 300 softcover, and 400 plastic books sold in Los Angeles. The bookstore chain actually 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 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

(a) Use matrix operations to determine the total sales over the 6 months, broken down by store and type of book.

Hard Soft Plastic
San Francisco
Los Angeles

(b) Use matrix operations to determine the inventory in each store at the end of June.

Hard Soft Plastic
San Francisco
Los Angeles
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
6 0

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

(a)

\left[\begin{array}{cccc}T&H&S&P\\S&600&1300&2000\\L&400&300&400\end{array}\right] = A.

In the above matrix A, the columns refers the three type of books and the rows refers the from which stores the books are been sold.

The numbers represents the corresponding sales in the month of January.

The sale is same for the 6 months.

Hence, 6A = \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right]. This matrix 6A represents the total sales over the 6 months.

(b)

If we denote the books in stock at the starting of January by B, then

B = \left[\begin{array}{cccc}T&H&S&P\\S&1000&3000&6000\\L&1000&6000&3000\end{array}\right].

Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

If we represent the amount restocked books at the end of each month by another matrix C, then

C = \left[\begin{array}{cccc}T&H&S&P\\S&500&1400&1400\\L&500&500&500\end{array}\right].

This restocking will be done for 5 times before the end of June.

If there would be no sale, then the stock would be

B + 5C = \left[\begin{array}{cccc}T&H&S&P\\S&1000+2500&3000+7000&6000+7000\\L&1000+2500&6000+2500&3000+2500\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right].

Since, the total sale is given by 6A, at the end of June, the inventory in each store can be shown as following,

B+5C-6A \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right] - \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&-100&2200&1000\\L&1100&6700&3100\end{array}\right]

You might be interested in
What is the answer 1 plus 1
AnnZ [28]

Answer:

the answer is 4, just kidding it's 2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Fill in the next entry in the pattern<br> 81, 27, 9, 3,
Dominik [7]
The answer to your problem is 1
6 0
3 years ago
Read 2 more answers
Order these numbers from least to greatest. <img src="https://tex.z-dn.net/?f=6%20%5Cfrac%7B1%7D%7B11%7D%20" id="TexFormula1" ti
andrezito [222]

We shall first of all, convert all the numbers to the same base. This means we either;

Convert the fractions to decimals OR

Convert the decimals to fractions

Let us therefore convert the decimals to fractions.

undefined

5 0
1 year ago
109/10 in simplest form explain
maksim [4K]
10 9/10.... because 10 can be divided into 109 10 whole times with a remainder of 9 so you put the 9 over the original denominator which is 10 so 9 over 10
4 0
3 years ago
Read 2 more answers
Use inductive reasoning to find the next term in the sequence 0, 1, 1, 2, 3, 5, 8 … What is the next term?
Anna007 [38]
13, each term is the sum of two preceding ones.
6 0
3 years ago
Other questions:
  • Prove the following
    9·1 answer
  • Which of the following is a mixed number? A. 5/2 B. 2.3 C. 2 1/2 D. 2/5
    14·2 answers
  • Carey is trying to decide between two guitars. The first had an original price of $160, but is on sale for $100. The second had
    13·1 answer
  • What is the value of x
    10·2 answers
  • Which is an x-intercept of the graphed function?
    15·1 answer
  • Use the number line to identify the least value, first quartile, median, third quartile, and greatest value of the data.
    10·2 answers
  • Ehelp help help help help
    5·1 answer
  • Hey yall, who wants a quick 20?
    14·2 answers
  • I’ll give out genius is someone can help me create a story about a graph pictured below!!
    10·2 answers
  • The body temperature of adults are normally distributed with a mean of 98.6 f and a standard deviation of 0.71f what temperature
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!