How many books should be shipped to each place?

Question

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 $9,200 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.)

 

(b) Is there a way of doing this for less money?

 

Answer 1

I tried to solve this with a matrix manipulation.

the matrix consisted of: b1 and b2 shipments from Brooklyn; q1 and q2 shipments from Queens, and each store in Long Island and Mahatten orders 1500 books.

b1 b2 q1 q2 Q

1 1 0 0 1000

1 0 1 0 1500

0 0 1 1 2000

0 1 0 1 1500

And these equations are not accurate, and after carefully checking them, I don't think the problem is solvable because what they order is not what can be shipped.