I need help with a word problem. Matrix form of system of equations

Question

I am having trouble with this word problem. I need to find the profit of both the San Francisco and Los Angles store. In January, the Left Coast Bookstore chain sold 700 hardcover books, 1,400 softcover books, and 2,500 plastic books in San Francisco; it sold 300 hardcover, 500 softcover, and 500 plastic books in Los Angeles. Now, hardcover books sell for $30 each, softcover books sell for $10 each, and plastic books sell for $15 each. Suppose that each hardcover book costs the stores $10, each softcover book costs $5, and each plastic book costs $10. Use matrix operations to compute the total profit at each store in January

Answer 1

I don't have the proper symbol for a matrix, but the numbers would look something like this.

 

                    income                                     cost                                      

| 700     1400   2500 |        *|  30  |      -  |  700   1400 2500  |      * |  10  |

| 300      500      500 |          |  10  |         |  300     500   500   |         |  5    |

                                               |  15  |                                                      |  10  |

 

Hope this makes some sense to you.

 

 

Answer 2

Hi Amanda--

 

I'm pretty sure "Matrix Operations" is what we old fogies used to call "making a chart..."

 

I would put a row for L.A., and a row for S.F.

 

then column heads for "# of hardcovers @$30; hardcover revenue;" etc. through the different kinds of books, the amount of revenue they earned at each store, AND a Total column. So it could look like this:

 

          #HC's @ 30$   HC revenue   #SC's @ 10$   SC revenue

L.A.             300            9000 $           500             5000$

S.F.

 

 

And just add on the columns for the plastic books at each store AND a Total column, fill in the other numbers, and add 'em up!

 

Then you can stick a grand-total box at the far end of the Total row.

 

Are you allowed to use a calculator for the multiplication and addition? (I'm guessing yes...)

 

"Matrix Operations," lolz... :-) Hope this is helpful...

 

Matt