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 shipping costs, we need to find the optimal distribution of textbooks from each warehouse to each school. This can be solved using linear programming.
Let's assume:
- x1 = number of books shipped from Massachusetts to the New Hampshire school
- y1 = number of books shipped from New York to the New Hampshire school
- x2 = number of books shipped from Massachusetts to the Vermont school
- y2 = number of books shipped from New York to the Vermont school
We can set up the following objective function to minimize the total shipping cost:
Minimize Z = 2x1 + 2.5y1 + 3x2 + 1.7y2
Subject to the following constraints:
x1 + y1 ≤ 70 (the total number of books available in the Massachusetts warehouse)
x2 + y2 ≤ 100 (the total number of books available in the New York warehouse)
x1 + y2 = 80 (the number of books ordered by the New Hampshire school)
x2 + y2 = 55 (the number of books ordered by the Vermont school)
Now we will solve this linear programming problem using a solver or linear programming software. The optimal solution will provide the number of books to be shipped from each warehouse to each school that minimizes the shipping costs.