Answer:
a)
Brooklyn to Long Island = 0 books
Brooklyn to Manhattan = 1000 books
Queens to Long Island books = 1500 books
Queens to Manhattan books = 500 books
b)
YES
Step-by-step explanation:
This is a equation's system with 4 unknown variables ( the number of the 4 kinds of shippings performed) , lets call the 4 variables like this:
- a: Brooklyn to Long Island books
- b: Brooklyn to Manhattan books
- c: Queens to Long Island books
- d: Queens to Manhattan books
Now, let´s see what we know:
1) First we know that each bookstore has asked for 1500 books so:
- 1500= b+d => b= 1500-d (1)
- 1500= a+c=> a= 1500-c (2)
2) We also know that the total amount spent in transportation is 9000$ at the given individual trasportattion prices
9000$= 5$*a+1$*b+4$*c+2$*d
=> 9000= 5a+b+4c+2d
=> c= (9000-5a-b-2d)/4 (3)
3) Finally, we know that the since we have a total number of books in the two warehouses of 3000 books, the same quantity that is demanded by the two bookstores, all the books are delivered.
So , in Brooklyn there are 1000 books that can be delivered to LI or Manhattan:
- 1000 = a+b => a= 1000-b (4)
and in Queens there are 2000 books:
- 2000 = c+d => d= 2000-c (5)
Now, formulas (2) and (4) are equal to a, so they are equal to each other
1000-b= 1500-c => b= c-500 (6)
Now lets solve by substitution in formula (3):
c= (9000-5a-b-2d)/4
=> 4c= 9000-5a-b-2d
=> 4c= 9000-5( 1500-c)- (c-500)-2*(2000-c)
=> 4c= -3000+6c =><em> c=1500</em>
Then:
- d= 2000-c= 2000-1500=><em> d=500.</em>
- b= c-500 => <em>b= 1000</em>
- a=<em> </em>1500-c <em>=> c= 0</em>
b) If we look at the trsnportation prices the cheaper is from Brooklyn to Manhattan, so lets try to maximize this tranportation.
In Brooklyn we have 1000 books, and we need 1500 in Manhattan, so lets do all the the shipping from brooklyn to Manhattan.:
- 1000 books *1 $/ book= 1000$
We will need 500 additional books from Queens at 2$/ book:
- 500 books * 2 $/book = 1000$
Then the 1500 books left in Queens will be shipped to Long Island at a price of 4$/ book:
- 1500 books * 4 $/book= 6000$
Total amount spent = 1000$+1000$+6000$ = 8000$
