Consider the following problem: min x +1 Subject tox22 (i)(1 mark) Determine the dual function fo...
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual problem graphically. Identify the corner- point feasible (CPF) solutions and comer-point infeasible solutions for both problems. Calculate the objective function values for all these values. Identify the optimal solution for Z. I 피 University 2b. For each of the following linear programming models write down...
Write down the associated dual problem. (ii)Given the information that the optimal basic variables are 1xand 3x, determine the associated optimal dual solution (1y, 2y and w). Maximize subject to z = x, +5x2 + 3x3 x, + x2 + x3 = 3 2x, - x2 = 4 *,,X, X, 20 (i) Write down the associated dual problem. (5 marks) (ii) Given the information that the optimal basic variables are x, and xz, determine the associated optimal dual solution (y,,...
how to do part A B and C? Use Lagrange multipliers to find the maximum and minimum values of the function f subject to the given constraints g and h f(x, y, z)-yz-6xy; subject to g : xy-1-0 h:ỷ +42-32-0 and a) (i)Write out the three Lagrange conditions, i.e. Vf-AVg +yVh Type 1 for A and j for y and do not rearrange any of the equations Lagrange condition along x-direction: Lagrange condition along y-direction: Lagrange condition along z-direction: 0.5...
1. Consider the constrained optimization problem: min f(x,x2) - (x-3)2 (x2 -3)2 Subject to Is this problem convex? Justify your answer Form the Lagrangian function. a. b. Check the necessary and sufficient conditions for candidate local minimum points. Note that equality constraint for a feasible point is always an active constraint c. d. Is the solution you found in part (c) a global minimum? Explain your answer
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the Lagrangian function for this individual. (2 marks) (6 marks) Using Cramer's rule, solve for x, y and 2. ii) Using Hessian matrix, check the second-order sufficient condition to verify that the utility of this individual is at maximum. (3 marks) S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the...
KKT is karush kuhn tucker Question 5 [15 marks] (Chapters 5, 6, 7 and 11) Consider the optimization problem min (r1,23)ER3 1 + 222 2a3 = 2, s.t. i) [2 marks] Is this problem convex? Justify your answer. ii) [3 marks] Can we say that this problem has an optimal solution? Justify your answer iii) [4 marks] Are the KKT optimality conditions necessary for this problem? In other words, given a KKT point of this problem, must it be an...
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...
if so, prove It. i 10. Consider the dual canonical tableau below: X, X, -1 Assume, without loss of generality, that a>0. a. Ifb>0 and c>0, which of the four types of behavior for dual canonical linear programming problems as given by the duality theorem is exhibited above. Prove your assertion. b. Repeat part a under the assumptions that b>0 and c<0. c. Repeat part a under the assumptions that b <0 and c>0 d. Repeat part a under the...
Please do it ASAP. I will upvote immediately. Thanks! Problem 3 (Convex Optimization): Consider a linear programming: min c'e s.t.Ax > b (1) x > 0 Find the dual problem of the linear programming and argue that: (1) If the primal is unbounded, then the dual is infeasible; (2) If the primal is infeasible, then the dual is either infeasible or unbounded. 1 Note that strong duality holds for a linear programming if either the primal or the dual is...
Consider the following production function for an economy: 1. Y=2K1/4L3/4 (a) Suppose the capital stock is K = 16 and its labour force is L = 1. Find: (i) GDP; (ii) the marginal product of capital; (iii) the real rental price of capital; (iv) labour's share of income. (b) Suppose further that aggregate consumption (C) is 80 per cent of disposable income, government spending is G = 1, the budget is balanced, and private sector investment is I = 6...