Hammertown Steel (HS) is planning raw materials requirements for a 40 metric ton (1 MT = 1,000 kg) order for steel it has received from a customer. HS can source ores from a number of suppliers and wants to ensure it minimizes its raw materials costs, while meeting the orders exacting product specifications.
All ores contain a mixture of various metals and waste. The following table summarizes the ores offered by various suppliers and the cost per metric ton (MT) of each:
Metal 1
Metal 2
Metal 3
Waste
Cost/MT
1
20%
11%
33%
36%
$36.00
Supplier
2
34%
15%
18%
33%
$38.00
3
22%
19%
28%
31%
$48.00
4
9%
14%
23%
54%
$25.00
5
17%
10%
24%
49%
$45.00
Refining eliminates all waste from the ore and the waste is sold to a gravel contractor for a net realizable value of $0. The contract for the steel has the following requirements:
1. The steel must contain at least 25% of metal 1
2. The steel must contain no more than 40% of metal 2
3. The steel may contain no less than 50% and no more than 70% of metal 3.
Write the linear program that will help the decision maker minimize the cost of raw materials needed to meet the requirements of this order.
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