Red bookstore wants to ship books from its warehouses in brooklyn and queens to its stores, one on long island and one in manhattan. its warehouse in brooklyn has 1,000 books and its warehouse in queens has 2,000. each store orders 1,500 books. it costs $5 to ship each book from brooklyn to long island and $1 to ship each book from brooklyn to manhattan. it costs $4 to ship each book from queens to long island and $2 to ship each book from queens to manhattan. (a) if red has a transportation budget of $8,460 and is willing to spend all of it, how many books should red ship from each warehouse to each store in order to fill all the orders? (assume red spends the entire transportation budget.)

red ships books from Brooklyn to long Island = 230

books from Queens to long Island   = 1270

books shipped from Brooklyn to Manhattan =  770

books shipped from from Queens to Manhattan  = 730

Step-by-step explanation:

Given:

Total books at Brooklyn warehouse = 1,000

Total books at Queens warehouse = 2,000

Books required = 1500 each

total transportation budget = $8460  

Costs of shipping each book from Brooklyn to Long Island = $5

Costs of shipping each book from Brooklyn to Manhattan = $1

Costs of shipping each book from Queens to Long Island = $4

Costs of shipping each book from Queens to  Manhattan = $2

let the books from Brooklyn to long Island = x

and, y books from Queens to long Island  

Therefore,

books shipped from Brooklyn to Manhattan = 1000 - x

and,

books shipped from from Queens to Manhattan  = 2000 - y

also,

x + y = 1500

or

x = 1500 - y (a)

also

total transport = $5x + $1(1000-x) + $4y + $2(2000-y) = $8460

or

5x + 1000 - x + 4y + 4000 - 2y = 8460

or

4x + 5000 + 2y = 8460

or

4x + 2y = 3460

or

2x + y = 1730  (b)

on solving (a) and (b)

2 × (1500 - y) + y = 1730

or

3000 - 2y + y = 1730

or

-y = -1270

or

y = 1270

therefore,

x = 1500 - 1270 = 230

hence,

red ships books from Brooklyn to long Island = x = 230

books from Queens to long Island   = y = 1270

books shipped from Brooklyn to Manhattan = 1000 - x = 1000 - 230 = 770

books shipped from from Queens to Manhattan  = 2000 - y = 2000 - 1270

= 730

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