Assignment 13 (December 10 - December 15)1. Let 22),(yxyxf, and we seek to maximize that function subject to constraint23)1(yx. Solve that problem with and without the additional Lagrange multiplier0. 2. Find the critical points in the problem of constrained optimization and classify themusing the second-order conditions: extrxyzzyxf),,(,subject to 0,1222zyxzyx.3. The weekly production of a factory depends on the amounts of capital and labor itemploys by the formula kllkq),(. The cost of capital is $4 per unit and the cost oflabor is $1. Find the minimum weekly cost of producing 200q.How the cost of production changes if the factory has to produce 202q?4. A firm’s inventory )(tIis depleted at a constant rate per unit time, i.e. txtI)(,where xis an amount of good reordered by the firm whenever the level of inventory iszero. The order is fulfilled immediately. The annual requirement for the commodity isAand the firm orders the commodity
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Optimization, Mathematical optimization, Constraint, lagrange multipliers, Joseph Louis Lagrange