Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 270 and the sum of the squares is a minimum. Step 1 Let f denote the sum of three positive numbers x, y, and z that is to be minimized subject to the constraint x + y + z = 270. Therefore, f(x, y, z) = x2 + y² + z? and g(x, y, z) = x + y + z - 270. Define a new function F as F(x, y, z, a) = f(x, y, z) – ig(x, y, z) - x2 + y2 + z2 – a(x + y + z – 270). - Find the partial derivatives of F with respect to x, y, z, and 2. F.(x, v, z, a) = 2x – · Z, F(x, y. z. a) = F.(x, y, z, a) = - (x + y + z – 270)
Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 270 and the sum of the squares is a minimum. Step 1 Let f denote the sum of three positive numbers x, y, and z that is to be minimized subject to the constraint x + y + z = 270. Therefore, f(x, y, z) = x2 + y² + z? and g(x, y, z) = x + y + z - 270. Define a new function F as F(x, y, z, a) = f(x, y, z) – ig(x, y, z) - x2 + y2 + z2 – a(x + y + z – 270). - Find the partial derivatives of F with respect to x, y, z, and 2. F.(x, v, z, a) = 2x – · Z, F(x, y. z. a) = F.(x, y, z, a) = - (x + y + z – 270)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 40E
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