1. The problem statement, all variables and given/known data
The Baraboo, Wisconsin plant of International Widget Co. uses aluminum, iron and magnesium to produce high-quality widgets. The quantity of widgets which may be produced using x tonnes of aluminum, y tonnes of iron and z tonnes of magnesium is Q(x,y,z) = xyz. the cost of raw materials is aluminum, $6 dollars per tonne; iron, $4 per tonne; magnesium, $8 per tonne. How many of each of aluminum, iron, and magnesium should be used to manufacture 1000 widgets at the lowest possible cost
2. Relevant equations
Q(x,y,z) = xyz is clearly the objective function
is the constraint 6x+4y+8z=1000 ?
3. The attempt at a solution
The Baraboo, Wisconsin plant of International Widget Co. uses aluminum, iron and magnesium to produce high-quality widgets. The quantity of widgets which may be produced using x tonnes of aluminum, y tonnes of iron and z tonnes of magnesium is Q(x,y,z) = xyz. the cost of raw materials is aluminum, $6 dollars per tonne; iron, $4 per tonne; magnesium, $8 per tonne. How many of each of aluminum, iron, and magnesium should be used to manufacture 1000 widgets at the lowest possible cost
2. Relevant equations
Q(x,y,z) = xyz is clearly the objective function
is the constraint 6x+4y+8z=1000 ?
3. The attempt at a solution
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