(2 marks) Solve (find the optimal point and objective function value at the optimal point) the...
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,...
(45 Points) Consider the constrained optimization problem: min f(x1, x2) = 2x} + 9x2 + 9x2 - 6x1x2 – 18x1 X1 X2 Subject to 4x1 – 3x2 s 20 X1 + 2x2 < 10 -X1 < 0, - x2 < 0 a) Is this problem convex? Justify your answer. (5 Points) b) Form the Lagrange function. (5 Points) c) Formulate KKT conditions. (10 Points) d) Recall that one technique for finding roots of KKT condition is to check all permutations...
Consider the following nonlinear program: min s.t. - (a) Express the objective function of the above problem in the standard quadratic function form: (b) Find the gradient and the Hessian of f(x). (c) If possible, solve the minimisation problem and give reasons why the solution you found is a global minimum rather than just a local minimum. Otherwise, demonstrate that the problem is unbounded. f (x: y) = (x + 2y)2-2x-y We were unable to transcribe this imageWe were unable...
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0
hi i need answer from part d
Question 2 (48 marks) Consider a firm which produces a good, y, using two factors of production, xi and x2 The firm's production function is Note that (4) is a special case of the production function in Question 1, in which α-1/2 and β-14. Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously...
15. | -12 points Find the optimal value(s) of the objective function on the feasible set S. z = 2x + 6y minimum maximum (0,6) (3, 4) 10.0" (5,0)
Find the indicated maximum or minimum value of the objective function in the linear programming problem. Maximize f - 30x + 40y subject to the following constraints. x + 2y = 48 x + y s 30 2x + y 50 x 20, y 20 Need Help? Read It Vatch It Talk to a Tutor -/12.5 POINTS HARMATHAP9 4.2.015.MI. EE Solve the following linear programming problem. Restrict x 20 and y 20. Maximize = 3x + 5y sub/ect to the...
Calculus 4
Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1) at the point (x,y) = (1,1). B) - 1 - 1 D)-i-j 10. . Find the largest value of the directional derivative of the function f(x,y) = ry + 2ya at the point (3,y) = (1,2). A) 53 ' B) V58 C) V63 D) 74 E) 85 y + The function (,y) = 2 + y2 + A) (-3,5), saddle point C) (-1,3), maximum...
Find the Maximum Value of an Objective Function Given Constraints by Graphing Question Solve the following maximization problem graphically. P(x, y 5x 2y subject to r 2 2 Select the correct answer below: O 30 48 O 22 O 28
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:...