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
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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
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