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- 1. using the diagonal, minors & cofactors, and pivotal method.1. Derive the dual linear program by using Lagrange duality.Can you show the step by step process of the first order conditions in order to get equation 8.9 , 8.10 and 8.11 Lagrange multipliers. L = Lagrangian Lagrange multipliers: Gamma and Lambda w_p = Portfolio weight
- 7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.I need solution about exercise 6 but need Hint. Consider the Laurent decomposition at each Z k, and use Exercise 5.A factory can produce two products, x and y, with a profit approximated by P=14x+22y−900P=14x+22y-900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x+2y≤1400x+2y≤1400. Identify the vertices of the feasible region. What production levels yield the maximum profit, and what is the maximum profit
- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, and u5. Then verify your solution.v = (5, 8, 7, −2, 4)u1 = (1, 1, −1, 2, 1)u2 = (2, 1, 2, −1, 1)u3 = (1, 2, 0, 1, 2)u4 = (0, 2, 0, 1, −4)u5 = (1, 1, 2, −1, 2)Sketch a graph of x=-3+2cos(t), y= -2+2sin(t), 0< t < 2piDetermine the value of x, y, and z using Gauss-Jordan Reduction Method
- Graph the points z=x+iy in |z|Consider the problem (attached image) min x2 subject to x2 = 1 x1, x2 ≥ 0 Write down its dual. For both the primal and the dual problem determine whether they have unique optimal solutions and whether they have nondegeneration optimal solutions.Compute the Wronskian for 2t^2y''+3ty'-y=0