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.