Question: operation resarch Q1. (5 points) Determine the extreme points (maximums/minimums) of the following function: f(x) = 2x12 + x2 + x32 + 6(x1 + x2

operation resarch

Q1. (5 points) Determine the extreme points (maximums/minimums) of the following function: f(x) = 2x12 + x2 + x32 + 6(x1 + x2 + x3) + 2X1XzX3 PLEASE SHOW YOUR WORK. Q2. (5 points) Solve the following linear programming problem by the Lagrangean method: Maximize f (X) = 5x1 + 3x2 subject to gi (X) = X1 + 2x2 + x3 - 6 = 0 g2 (X) = 3x1 + x2 + x4-9 = 0 X1, X2, X3, X40 Remark: you need to find the extreme points (maximums/minimums) using necessary and sufficient conditions, (PLEASE SHOW YOUR WORK). Q3. (5 points) Carry out at most five iterations for the following problem using the method of steepest ascent. Assume that X = (0,0). min f(x) = (x2 X1?)2 + (1 - X1)? PLEASE SHOW YOUR WORK. Q4. (5 points) Solve the following problem by the linear combinations method Minimize f(x) = x1 + x2 - 3 X1 X2 subject to 3x1 + x2

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