A chemical company wishes to mix three elements (E, F, and G) to create three alloys (X, Y, and Z). The costs of
The elements are as shown in the following table.
To maintain the required quality for each alloy, it is necessary to specify certain maximum or minimum percentages of the elements. These are as shown in the following table.

The usage of each element is limited to 5,000 tons, and the total usage of all three elements is limited to 10,000 tons. Further, due to the relatively uncertain demand for alloy Z, the company would like to ensure that Z constitutes no more than 30% of the total quantity of the three alloys produced. Determine the mix of the three elements that will maximize profit under these conditions.

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SELLING ALLOY SPECIFICATIONS PRICE PER TON $5.50 No more than 30% of Eat least 40% ofF, no more than 5090 of G No more than 50% of Eat least 10% ofF Y $4.00 $6.00 No more than 70% of E, at least 20% ofG