An appliance company has two warehouses and two retail outle

An appliance company has two warehouses and two retail outlets. Warehouse A has 400 refrigerators, and warehouse B has 300 refrigerators. Outlet I needs 200 refrigerators, and outlet II needs 300 refrigerators. It costs $36 to ship a refrigerator from warehouse A to outlet I and $30 to ship a refrigerator from warehouse A to outlet II. It costs $30 to ship a refrigerator from warehouse B to outlet I and $25 to ship a refrigerator from warehouse B to outlet II. How should the company ship the refrigerators to minimize the cost?

The company should ship the refrigerators using warehouse B to minimize cost. Here is why:

36=A-Outlet I
30=A-Outlet II

30=B-Outlet I
25=B-Outlet 11

200x30=6000
100x25=2500
200x30=6000
Total=14500

Explain this answer above to me or is it wrong? Please clarify

Solution

Here we have two case scenarios which is further divided into 4.
First let us check how many cases are there:
Case 1: Outlet 1 and Outlet 2 both are supplied by Warehouse A

Case 2: Outlet 1 and Outlet 2 both are supplied by Warehouse B

Case 3: Outlet 1 is supplied by Warehouse A and Outlet 2 is supplied by Warehouse B

Case 4: Outlet 1 is supplied by Warehouse B and Outlet 2 is supplied by Warehouse A

Case 5: Where the items are mixed and supplied to A & B

So let us analyse all the cases and check which condition gives us the minimum cost.

To know the minimum cost we will consider Case 5:

data given to us is :
36=A-Outlet I
30=A-Outlet II

30=B-Outlet I
25=B-Outlet 11

from here it is prominent that Warehouse B is cheaper than Warehouse A.
But there is a problem the total number of items present in Warehouse B is 300 whereas our requirement is 500.
So we need to get some products from Warehouse A also. From the data above we need to check which product is cheaper in Warehouse A . So Outlet II supply will cost $30 and Outlet I wil cost $36.
Obviously then we will use Outlet II product.

Calculation part :

Outlet 1 needs 200 so total cost is 200x30=6000 ( total nomber of product X price of transportation)

Outlet 1 needs are fulfilled now let us concentrate on outlet 2.
So Outlet 2 will get 100 products from Warehouse B and 200 Products from Warehouse A.
so cost for that is 100x25=2500 ; 200x30=6000

Total cost adds up to $ 14,500.

You can check this for all the other cases keeping in mind the number of items present in the warehouse and number items to be supplied.