An appliance company has two warehouses and two retail outlets. Warehouse A has
ID: 3420630 • Letter: A
Question
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
Explanation / Answer
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.