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MATHEMATICAL PROGRAMMING AND ITS APPLICATIONS TO MANAGEMENT SCIENCE Buratto Alessandra Facoltà for Economia for Padova 1 PRODUCTION occupation - thrills A rm produces two display cases of belts: A & B. Type A is better for quality with respect to B. The net prot is 2 Euros for event A and 1,5 Euros for type B. Time necessary for production is excessively dierent: 10 momentutes for a type A belt and 5 minutes for a type B belt. all day 5000 minutes for production are available. Inventory origin of leather permits to produce 800 belts a day (both type A and B). Every day is possible to use 400 buckles for type A and 700 buckles for type B. How many belts, of each type, the rm has to produce in order to maximize the total net prot? 2 PRODUCTION PROBLEM xi ? IR + production factor ith, i = 1, . . . , n; f (x1, x2, . . . , xn) p ci marginal price ; marginal cost production function , of factor ith, i = 1, . . . , n; maximize pf (x)?(c1x1 + c2x2 + . . . + cnxn) c·x maximize pf (x) ? c x. 3 PRODUCTION PROBLEM with xed cost (C) for the production factors maximize subjected to pf (x) ? cx, cx = C.

4 TRANSPORT PLAN m warehouses, each one with a given quantity of product ai n distributors/shops, each one with a given demand bj Objective: Trasporting the required quantities of product from the warehouses to the shops minimizing transport costs. 5 min s.t. m i=1 n j=1 m i=1 n j=1 cij xij xij ? ai, xij = bj , i = 1, .., m j = 1, .., n j = 1, .., n. xij ? 0, i = 1, .., m, 6 MATHEMATICAL PROGRAMMING OPTIMIZATION max/min f (x) s.t. x ? X ? IR n If X = IR n ? unconstrained computer programing nec. cond. concavity /convexity topical anesthetic/global Theor 1st/2nd order If X ? IR n ? constrained programming a) Classical programming (Lagrange) (only equality constraints) b) NonLinear programming (P.N.L.) (equality and inequality constraints) c) Linear programming (P.L.) (linear functions and linear... If you want to get a full essay, order it on our website: Orderessay

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