30 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.

ELEMENT COST PER TON E $3.00 F $4.00 G $3.50 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.

ALLOY SPECIFICATIONS SELLING PRICE PER TON X No more than 30% of E, at least 40% of F, no more than 50% of G

$5.50 Y No more than 50% of E, at least 10% of F

$4.00 Z No more than 70% of E, at least 20% of G

$6.00 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.