Ag Bus 313 Homework 2 100 Points Tentative Due Date: Noon on 1/31/19 Dr. Hurley Directions: Please answer all items on this homework. You must show all your work. Unless otherwise stated, please simplify your answer. Find the first order and second order (this includes the cross partial derivatives) partial derivatives of the following functions with respect to x1 and x2: (20 Points) y = f(x1,x2) = 45x1x2 y = f(x1,x2) = 4x12 + 3x1x2 + 2x22 y = f(x1,x2) = x11/3x22/3 y = f(x1,x2) = (x1x2) 3/4 Use the first order conditions to find the critical points of the function. Use the second order conditions to show whether the critical points are maximum, minimum, or saddle points (point of inflection). Are the critical points relative or absolute extrema? Please explain. (40 Points) y = f(x) = + 8x + 32 –4x2 y = f(x) = 6x2 + 36x + 15 y = f(x) = 2x3 + 6x2 + 6x + 2 y = f(x) = + 24x + 45 –2x3 y = f(x) = 4)2 –(x2 – Minimize f(x1,x2) = 4x1 + 27x2 subject to the constraint 300 = g(x1,x2) = x11/3x22/3. solve this problem using the Lagrange Method. Next, resolve this problem by changing it into an unconstrained minimization problem. (20 Points) Maximize f(x1,x2) = x12/3x21/3 subject to the constraint 16,200 = g(x1,x2) = 54x1 + 8x2. First solve this problem using the Lagrange Method. Next, resolve this problem by changing it into an unconstrained maximization problem. (20 Points)
Ag Bus 313 Homework 2 100 Points Tentative Due Date: Noon on 1/31/19 Dr. Hurley Directions: Please answer all items on this homework. You must show all your work. Unless otherwise stated, please simplify your answer. Find the first order and second order (this includes the cross partial derivatives) partial derivatives of the following functions with respect to x1 and x2: (20 Points) y = f(x1,x2) = 45x1x2 y = f(x1,x2) = 4x12 + 3x1x2 + 2x22 y = f(x1,x2) = x11/3x22/3 y = f(x1,x2) = (x1x2) 3/4 Use the first order conditions to find the critical points of the function. Use the second order conditions to show whether the critical points are maximum, minimum, or saddle points (point of inflection). Are the critical points relative or absolute extrema? Please explain. (40 Points) y = f(x) = –4x2 + 8x + 32 y = f(x) = 6x2 + 36x + 15 y = f(x) = 2x3 + 6x2 + 6x + 2 y = f(x) = –2x3 + 24x + 45 y = f(x) = –(x2 – 4)2 Minimize f(x1,x2) = 4x1 + 27x2 subject to the constraint 300 = g(x1,x2) = x11/3x22/3. solve this problem using the Lagrange Method. Next, resolve this problem by changing it into an unconstrained minimization problem. (20 Points) Maximize f(x1,x2) = x12/3x21/3 subject to the constraint 16,200 = g(x1,x2) = 54x1 + 8x2. First solve this problem using the Lagrange Method. Next, resolve this problem by changing it into an unconstrained maximization problem. (20 Points)
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