Question by Gham: Edwards Manufacturing Company purchases two component parts from three different suppliers.?
The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:
Component 1 2 3
1 $ 12 $ 13 $ 14
2 $ 10 $ 11 $ 10
Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows.
Supplier 1 2 3
Capacity 600 1000 800
If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component 2, how many units of each component (C1, C2) should be ordered from each supplier (S1, S2, S3)?
What is the total purchase cost for the components?
Answer by Meng tian
In short, for each component, we should look for the supplier offering the lowest price.
For component 1, that will be supplier 1.
For component 2, that will be supplier 1 and 3.
However, since we need to buy component 1 from supplier 1 as well, so we should buy component 2 from supplier 3 instead.
We need 1000 units of component 1.
Supplier 1 only provide us with 600 units.
For the other 400 units, it must come from the supplier who offer the next lowest price, which is supplier 2.
Thus, we will get the remaining 400 units of component 1 from supplier 2.
Supplier 3, on the other hand, will provide us with all 800 units of component 2.
The amount we will pay supplier 1 is:
$ 12 x 600 = $ 7200
The amount we will pay supplier 2 is:
$ 13 x 400 = $ 5200
The amount we will pay supplier 3 is:
$ 10 x 800 = $ 8000
Hence, the total purchase cost is:
$ 7200 + $ 5200 + $ 8000 = $ 20400
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