F(X,Y) =y^4 +x^3 - 2xy^2 - x f(x,y) = 2x^3 y - y^2 - 3xy f (x,y,z) = yz - xyz -
ID: 2859586 • Letter: F
Question
F(X,Y) =y^4 +x^3 - 2xy^2 - x f(x,y) = 2x^3 y - y^2 - 3xy f (x,y,z) = yz - xyz - x^2 - y^2 - 2z^2 f (x,y,z,w) = yw - xyz - x^2 - y^2 - 2z^2 f(x,y,z,w) = yw - xyz - x^2 - 2z^2 + w^2 show that the largest rectangular box having a fixed surface area must be a cube. What point on the plane 3x - 4y - z = 24 is close to the origin? Find the points on the surface xy +z^2 = 4 that are closest to the origin. Be sure to give a convincing argument that your answer is correct. Suppose that you are in charge of manufacturing two types of television sets. The revenue function in dol.Explanation / Answer
Answer (29):
As a Lagrange multiplier problem, we see the function to be minimized is distance squared from (x, y, z) to the origin (0, 0, 0), i.e. f(x, y, z) = x^2 + y^2 + z^2 . Our constraint is g(x, y, z) = 3x 4z z = 24. Solving the system of equations f = g, g(x, y, z) = c, we get = 24 /13 , so x = 36 /13 , y = 48 /13 , z = 12 /13 .
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