Automated Best Trade |

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Theoretical basic |

MATHEMATICAL MODEL - OR WHAT DOES IT DO? Trading company has the domestic market (XS) (synchoronized columns, rows) available for purchase: q(1,1), ..., q(i,j), ..., q(r,n) units; (r) types of articles X(1), ..., X(i), ..., X(r) of the (n) number of clients S(1), ..., S(j), ..., S(n); at prices p(1,1), ..., p(i,j), ..., p(r,n) monetary units. So, trading company that can supply most: Q(1), ..., Q(i), ..., Q(r) units, (r) the type of article X, (n) the number of clients S, according to the average prices of P(1), ..., P(i), ..., P(r). See images 1. and 2. Mathematical model (symbolic) Thus, the domestic market (XS), purchased articles X can sell to foreign market (XC), (m) the number of clients C(1), ..., C(k), ..., C(m), where client C(k) can sell the most w(i,k) units of articles X(i) at a price t(i,k). Of course, company can not sell more articles X(i) the foreign market than it is purchased on the domestic market or to buy more on the domestic than it can sell to foreign ie. Q(i) = W(i). Thus, the foreign market sizes exist: the required amount of W(1), ..., W(i), ..., W(r); articles X(1), ..., X(i) ..., X(r); the average is prices P(1), ..., P(i), ..., P(r). See images 1. and 2. Mathematical model (symbolic), again Also, trading company, has the foreign market (YC) (synchoronized columns, rows), available for purchase: z(1,1), ..., z(f,o), ..., z(g,m) units, (g) type of articles Y(1), ..., Y(f), ..., Y(g) of the same or different (m) number of clients C(1), ..., C(o), ..., C(m), where the client C(o) for the quantity z(f,o) units of articles Y(f) due to the cost of u(f,o) monetary units. So, trading company, that can supply most: Z(1), ..., Z(f), ..., Z(g) units, (g) the type of article Y, (m) the number of clients C, according to the average prices of U(1), ..., U(f), ..., U(g). See images 1. and 2. Mathematical model (symbolic), again Thus, the foreign market (YC), purchased articles Y can sell to domestic market (YS), (n) the number of different or the same clients S(1), ..., S(h), ..., S(n), where the client (h) can sell the most d(f,h) units of articles Y(f) at a price e(f,h). Of course, company can not sell more articles Y(f) on the domestic market than it was purchased in foreign markets or in foreign buy more than they can sell in the domestic ie. Z(f) = D(f). Thus, the size of the domestic market exist: the quantity demanded D(1), ..., D(f), ..., D(g); articles Y(1), ..., Y(f) ..., Y(g); the average is in the prices U(1), ..., U(f), ..., U(g). See images 1. and 2. Mathematical model (symbolic), and again You see. How easy is that! Of course, the problem can be reduced to the right or the left half, then only the articles Y or X. See image 3. Reduced mathematical model (symbolic) PROBLEM: "With this information in a commercial undertaking is a problem of optimization, what amount of certain types of articles to buy and sell on the markets and the clients to whom the given circumstances made the most profit?" SOLUTION: This is a linear programming problem which is solved by Simplex method by George Dantzig. In other words, it is 'Trade as Antagonistic Matrix Game' with complex conditions where the program delivers optimum business decision that maximizes profit. INITIAL IDEA: Prof. Dr. Alojzij Vadnal "The application of mathematical methods in economics", "Informator" - Zagreb NOTE: For individual label size quantity and price index is the first article (synchoronized columns), and the second is the client (rows). |

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Mathematical model (symbolic) |

Mathematical model (symbolic) |

Reduced mathematical model (symbolic) |