A manufacturing company has three plants, I, II and III, which produce x, y, and z units, respectively, of a

certain product. The annual revenue from this production is given by

R(x, y, z) = 6xyz^2 − 400000(x + y + z)

If the company is to produce 1000 units anually, use Lagrange Multipliers to determine how it should allocate

production among the three plants so as to maximize its revenues.