Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.
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- Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the planes 2x-y = 0 and y + z = 0 Can this problem be solved using lagrange multipliers?By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1 and u = y2, find the minimum distance in the xy-plane from the line y = x + 1 to the pa-rabola y2 = x.