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:

Develop an LP model to determine the optimal input mix the foundry should smelt, and find the solution using Lingo and excel solever