Question

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?

Answer 1

Given :  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

To find :  How many copies should the company ship from each warehouse to each school to minimize the shipping costs on these two orders

Solution:

Let say x  books   from Massachusetts   ware house to  New Hampshire school  & y  books to  Vermont school  

x , y  ≥ 0

x + y  ≤  70    

y ≤ 55

then 80 - x  books from newyork to New Hampshire school

&  55 - y  books from  newyork to  Vermont school  

80 - x + 55 - y  ≤ 100

=> x + y  ≥ 35  

Total cost  =  2x   + 3y  +   2.5(80-x) +  1.7(55-y)

=   200 + 93.5  + 1.3y  - 0.5x

= 293.5  + 1.3y  - 0.5x

y = 55 ,  x   = 15

Cost = 293.5  + 1.3*55  - 0.5*15 =  357.5

y = 55 ,  x   = 0

Cost = 293.5  + 1.3*55  - 0.5*0 =  365

y  = 35     , x = 0

Cost = 293.5  + 1.3*35  - 0.5*0 =  339

y = 35  , x  = 35

Cost = 293.5  + 1.3*35  - 0.5*35 =  321.5

y = 0  , x  = 70

293.5  + 1.3*0  - 0.5*70 =   258.5  

258.5  is lowest cost

70 books to be shipped from   Massachusetts   ware house to  New Hampshire school

10 books from newyork to New Hampshire school

55 books from newyork to  Vermont school  

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