We have subject to the constraint g(x,y,z)=x+y+z-1000[/tex]
....[1]
...[2]
...[3]
Equate [1] and [2]:
Equate [1] and [3]:
Sub into the constraint:
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.