Red Bookstore wants to ship books from its warehouses in Bro

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 $8,240 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.)

Solution

No of books in Brooklyn warehouse = 1,000

No of books in Queens warehouse = 2,000

Order from Kong Island and Manhattan store = 1,500

Shipping cost from Brooklyn to Long Island = $5

Shipping cost from Brooklyn to Manhattan = $1

Shipping cost from Queens to Long Island = $4

Shipping cost from Queens to Manhattan = $2

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Start ordering as many books as possible with the lowest cost - Brooklyn to Manhattan($1)

Cost to ship 1,000 books from Brooklyn to Manhattan = 1 *1000 = $1,000

Since Brooklyn has 1,000 books we can use no further

Next is Queens to Manhattan since it costs $2

No of books to ship to Manhattan = 1500 - 1000 = 500

Cost to ship 500 books from Brooklyn to Manhattan = 2 *500 = $1,000

Next is Queens to Long Island since it costs $4

No of books to ship to Manhattan = 1500

Cost to ship 500 books from Brooklyn to Manhattan = 4 * 1,500 = $6,000

Total cost = $1,000 + $1,000 + $6,000 = $8,000 which is less than the transportation budget of $8,240