Question: Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at lest 21% of metal A, no more than 12% of metal B, no more than 7% of metal C, and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each of the six ores and the level of impurities in each ore are provided in the following table.

When the metals are processed and refined, the impurities are removed.

The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.

a. Formulate a linear programming model for this problem.