Aluminum, iron and magnesium are used to manufacture certain metal parts.The quantity of parts produced from...

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Aluminum, iron and magnesium are used to manufacture certainmetal parts.The quantity of parts produced from x tons of aluminumy tons of iron and z tons of magnesium is Q (x, y, z) = xyz.Aluminum is $ 800 per ton, iron is $ 400 per ton, and magnesium is$ 600 per ton.

use the Lagrange multiplier method to determine the number of tons of each material that must be used to manufacture 5000 metal parts at the lowest possible cost.

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Solution Given thequantity Q of the metal parts produced from x y and z tons ofaluminum iron and magnesiumSince aluminum iron and magnesiumare 800 400 and 600 per ton therefore the cost function Cwill be given by1Now the See Answer

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