a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX). a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
22. Tim (x,y) = (0,0) 2x² + 3y? x2 + +y? o 3 None of these 1 2
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9. Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9 Solve the following problem using Lagrange...
Q4: Solve the payoff matrix Example-1 Player B П I III IV V -2 0 0 5 Player A III II 3 2 2 7 4 0 -2 6 IV 5 3 4 2 -6 Q5: Determine the maximum and minimum values of the function: f(x)= 12x-45x 40x' +5 Q6: Find the second order Taylor's series approximation of the function ) =x}x, +xe about the point х*- Q7: Find the extreme points of the function f(x,x)xx+2x + 4x +6 Q8:...
please answer step by step Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2-1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above changed to: (3) (4) constraints are 2x-0.9y-z 2 x2+y2-0.9. Solve the...
21. [-14 Points] DETAILS TANAPCALC10 8.R.037. Use the method of Lagrange multipliers to optimize the function subject to the given constraints. Find the maximum and minimum values of the function f(x, y) = 2x – 3y + 1 subject to the constraint 2x2 + 3y2 – 320 = 0. At what point does the maximum occur? (x, y) = =( What is the value of f(x, y) at this point? f(x, y) = At what point does the minimum occur?...
Need help with this two questions 1. Consider the isoperimetric problem: = / yV1+y2da= min, y(0) y(a)0 subject to the constraint J = Jo In class we showed that this problem could be written as the solution of the ODE A VI2 where A is a constant and A is the Lagrange multiplier a) Show very clearly that the general solution of this equation can be written as B y A - Acosh b) Determine the values of A, A,...
Consider the following linear programming problem: Minimize 20X + 30Y Subject to: 2X + 4Y ≤ 800 6X + 3Y ≥ 300 X, Y ≥ 0 What is the optimum solution to this problem (X,Y)? A) (0,0) B) (50,0) C) (0,100) D) (400,0)
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.