9. A foundry smelts steel, aluminum, and cast iron scraps to produce two types of metal ingots, I and II, with specific limits on the aluminum, graphite and silicon contents. Aluminum and silicon briquettes may be used in the smelting process to meet the desired specifications. The following tables set the specifications of the problem:

Contents (%)

Input item Aluminum Graphite Silicon Cost/ton ($) Available tons/day Steel scrap 10 5 4 100 1000 Aluminum scrap 95 1 2 150 500 Cast iron scrap 0 15 8 75 2500 Aluminum briquette 100 0 0 900 Any amount Silicon briquette 0 0 100 380 Any amount 2.3 Ingot I Ingot II

. Ingredient Aluminum Graphite Silicon Demand (tons/day)

Minimum 8.1%

1.5%

2.5%

130 Maximum 10.8%

3.0%

00 Minimum 6.2%

4.1%

2.8%

250 Maximum 8.9%

00 4.1%

Determine the optimal input mix the foundry should smelt.

2.3 Selected LP Applications 57