Two High Schools ordered AP Chemistry text book from the same book store. A New Hampshire school has ordered 80 copies, while a Vermont school ordered only 55 copies. The store has 70 books in its warehouses in Massachusetts and 100 books in the other warehouse in New York. Shipping one copy from Massachusetts to New Hampshire costs $2 and from Massachusetts to Vermont costs $3. Shipping from New York’s warehouse is respectively $2.5 and $1.7. How many copies should the company ship from each warehouse to each school to minimize the shipping costs on these two orders?
To minimize the shipping costs for the two orders, we need to find the optimal distribution of books from each warehouse to each school.
Let's start by considering the number of books each school needs and the available stock in each warehouse:
- New Hampshire school needs 80 copies
- Vermont school needs 55 copies
- Warehouse in Massachusetts has 70 books
- Warehouse in New York has 100 books
To minimize shipping costs, we will consider two scenarios: shipping from Massachusetts and shipping from New York.
1. Shipping from Massachusetts:
a. Determine the maximum number of copies that can be shipped from Massachusetts to each school:
- From Massachusetts to New Hampshire: Maximum 70 (books in stock in Massachusetts)
- From Massachusetts to Vermont: Maximum 55 (books needed by Vermont)
b. Calculate the remaining copies needed for each school:
- Remaining copies for New Hampshire: 80 - 70 = 10
- Remaining copies for Vermont: 55 - 55 = 0
c. Calculate the number of copies to be shipped from Massachusetts to each school:
- From Massachusetts to New Hampshire: 10
- From Massachusetts to Vermont: 55
2. Shipping from New York:
a. Determine the maximum number of copies that can be shipped from New York to each school:
- From New York to New Hampshire: Maximum 100 (books in stock in New York)
- From New York to Vermont: Maximum 55 (books needed by Vermont)
b. Calculate the remaining copies needed for each school:
- Remaining copies for New Hampshire: 80 - 100 = 0
- Remaining copies for Vermont: 55 - 55 = 0
c. Calculate the number of copies to be shipped from New York to each school:
- From New York to New Hampshire: 80
- From New York to Vermont: 55
Now, let's compare the shipping costs for each scenario:
1. Shipping from Massachusetts:
- Cost of shipping 10 copies from Massachusetts to New Hampshire: 10 * $2 = $20
- Cost of shipping 55 copies from Massachusetts to Vermont: 55 * $3 = $165
Total shipping cost from Massachusetts: $20 + $165 = $185
2. Shipping from New York:
- Cost of shipping 80 copies from New York to New Hampshire: 80 * $2.5 = $200
- Cost of shipping 55 copies from New York to Vermont: 55 * $1.7 = $93.5
Total shipping cost from New York: $200 + $93.5 = $293.5
Based on the calculations, the company should ship 10 copies from Massachusetts to New Hampshire and 55 copies from Massachusetts to Vermont to minimize the shipping costs on these two orders.