Question

A company produces steel boxes at 3 plants in amounts x, y, z respectively.producing an annual revenue amounts modeled by f(x, y, z)=4*x^3*y*z-100*(2*x-y+2*z).the company is to produce 100 units annually,then how should the production be distibuted to maximize the revenue

Answer 1

A company produces steel boxes at 3 plants in amounts x, y, z respectively.producing an annual revenue amounts modeled by f(x, y, z)=4*x^3*y*z-100*(2*x-y+2*z).the company is to produce 100 units annually,then how should the production be distibuted to maximize the revenue

Step-by-step explanation:

Here, g(x, y, z) = x + y + z − 100. The Lagrange multiplier method implies that

4x3z2 − 200 =

λ, 4x3z

2 − 200 = λ, 8xyz − 200 = λ and x + y + z − 100 = 0. These imply that

x = y, z

= 2x and

x = 25