Ass - 13 new.doc - Assignment 13(December 10 December 15 1 Let f x y x 2 y 2 and we seek to maximize that function subject to constraint x 1 3 y 2 Solve

# Ass - 13 new.doc - Assignment 13(December 10 December 15 1...

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Assignment 13 (December 10 - December 15) 1. Let 2 2 ) , ( y x y x f , and we seek to maximize that function subject to constraint 2 3 ) 1 ( y x . Solve that problem with and without the additional Lagrange multiplier 0 . 2. Find the critical points in the problem of constrained optimization and classify them using the second-order conditions: extr xyz z y x f ) , , ( , subject to 0 , 1 2 2 2 z y x z y x . 3. The weekly production of a factory depends on the amounts of capital and labor it employs by the formula kl l k q ) , ( . The cost of capital is \$4 per unit and the cost of labor is \$1. Find the minimum weekly cost of producing 200 q . How the cost of production changes if the factory has to produce 202 q ? 4. A firm’s inventory ) ( t I is depleted at a constant rate per unit time, i.e. t x t I ) ( , where x is an amount of good reordered by the firm whenever the level of inventory is zero. The order is fulfilled immediately. The annual requirement for the commodity is A and the firm orders the commodity

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• Spring '16
• Robert Stavins
• Optimization, Mathematical optimization, Constraint, lagrange multipliers, Joseph Louis Lagrange
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