Answer:
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
