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Linear programming

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming. More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints, its feasible region is a convex polytope, a set defined as the intersection of finitely many half spaces, each of, defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where this function has the smallest value if such a point exists. Linear programs are problems that can be expressed in canonical form as Maximize c T x subject to A x ≤ b and x ≥ 0 where x represents the vector of variables, c and b are vectors of coefficients, A is a matrix of coefficients, T is the matrix transpose; the expression to be maximized or minimized is called the objective function.

The inequalities Ax ≤ b and x ≥ 0 are the constraints which specify a convex polytope over which the objective function is to be optimized. In this context, two vectors are comparable. If every entry in the first is less-than or equal-to the corresponding entry in the second it can be said that the first vector is less-than or equal-to the second vector. Linear programming can be applied to various fields of study, it is used in mathematics, to a lesser extent in business and for some engineering problems. Industries that use linear programming models include transportation, telecommunications, manufacturing, it has proven useful in modeling diverse types of problems in planning, scheduling and design. The problem of solving a system of linear inequalities dates back at least as far as Fourier, who in 1827 published a method for solving them, after whom the method of Fourier–Motzkin elimination is named. In 1939 a linear programming formulation of a problem, equivalent to the general linear programming problem was given by the Soviet economist Leonid Kantorovich, who proposed a method for solving it.

It is a way he developed, during World War II, to plan expenditures and returns in order to reduce costs of the army and to increase losses imposed on the enemy. Kantorovich's work was neglected in the USSR. About the same time as Kantorovich, the Dutch-American economist T. C. Koopmans formulated classical economic problems as linear programs. Kantorovich and Koopmans shared the 1975 Nobel prize in economics. In 1941, Frank Lauren Hitchcock formulated transportation problems as linear programs and gave a solution similar to the simplex method. Hitchcock had died in 1957 and the Nobel prize is not awarded posthumously. During 1946–1947, George B. Dantzig independently developed general linear programming formulation to use for planning problems in the US Air Force. In 1947, Dantzig invented the simplex method that for the first time efficiently tackled the linear programming problem in most cases; when Dantzig arranged a meeting with John von Neumann to discuss his simplex method, Neumann conjectured the theory of duality by realizing that the problem he had been working in game theory was equivalent.

Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. In the post-war years, many industries applied it in their daily planning. Dantzig's original example was to find the best assignment of 70 people to 70 jobs; the computing power required to test all the permutations to select the best assignment is vast. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the simplex algorithm; the theory behind linear programming drastically reduces the number of possible solutions that must be checked. The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems. Linear programming is a used field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems.

Certain special cases of linear programming, such as network flow problems and multicommodity flow problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems. Ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality and the importance of convexity and its generalizations. Linear programming was used in the early formation

Bruce Inkango

Bruce Pascal Inkango is a French-Congolese former footballer. He played as a forward. Born in Poitiers, Inkango began his career at AS Cannes. On 21 September 2010, Inkango joined English side Gillingham of League Two, signing a three-month deal, he earned just six appearances with the Gills and left the club on 20 December, when his contract expired. Early 2011, Inkango signed for Albanian Superliga side KS Kastrioti. Whilst at the Albanian club, he found some of the best scoring form of his career. Inkango finished as the top goalscorer for Kastrioti in the 2011–12 season with 14 goals, scoring a total of 21 goals for one-and-a-half-year. In July 2012, Inkango joined Oțelul Galați in Romania, he made his Liga I debut in a 1–1 home draw against Rapid București on 30 July, coming on as a substitute for Laurențiu Buș. He was released by Oțelul on 31 January 2013. On 4 April 2013, Inkango signed a contract with Bulgarian A PFG club Cherno More Varna, he made his debut on 6 April, coming off the bench on the 69th minute to replace Simeon Raykov in a 3–1 away loss against Botev Plovdiv.

After a spell playing in Turkey for Denizlispor, Inkango signed for East Fife in March 2014. He was released by the club in May 2014. Bruce Inkango at Soccerbase Bruce Inkango at Soccerway Profile at

Massachusetts General Hospital, Bulfinch Building

The Bulfinch Building of the Massachusetts General Hospital is located on the hospital's main campus on Fruit Street in the West End of Boston, Massachusetts. It was designed by architect Charles Bulfinch, built between 1818 and 1823, with a major expansion in 1844-46. A National Historic Landmark, it is an excellent example of Classical Revival architecture, a rare surviving example of an early 19th-century public hospital building; the building is home to the Ether Dome, an operating theater, separately designated a National Historic Landmark as the site of the first public demonstration of the use of ether as an anesthetic. The Bulfinch Building is a rectangular structure, two stories in height, with a massive Ionic portico at the center of its longer facade; the building is built out of white granite from Chelmsford and stands on a basement of rusticated granite. It has a hipped roof, the central portion has a square attic story with chimneys at the corners and a saucer-shaped dome in the center.

The interior has undergone extensive and repeated renovations, as the hospital's needs for the space have changed. As designed by Charles Bulfinch in 1817 and built over the next five years by Alexander Parris, the building had smaller wings, had a capacity of 73 beds; the stonework for its construction was done by the inmates at the Charlestown Prison. The building's capacity was nearly doubled in 1844-46 by the addition of five bays to each of the wings, the original entrance hall designed by Bulfinch was extensively altered. Bulfinch's design, with an operating amphitheater under the dome, was based on that in the Pennsylvania Hospital building, which he saw on a visit in 1816; that amphitheater, now known as the Ether Dome, is where the first public demonstration of the use of ether as an anesthetic took place on October 16, 1846. The amphitheater was designated a National Historic Landmark in 1965 in recognition of this event; the entire building was listed on the National Register of Historic Places, designated a National Historic Landmark, in 1970, as an excellent example of Classical Revival architecture, as one of the oldest public hospital buildings in the nation.

The building is now surrounded by the much larger modern facilities of the hospital. List of National Historic Landmarks in Boston National Register of Historic Places listings in northern Boston, Massachusetts

Carlota Cove

Carlota Cove is the 1.9 km wide cove indenting for 1.14 km the northwest coast of Alfatar Peninsula, Robert Island in the South Shetland Islands, Antarctica next east of Coppermine Peninsula, entered between Fort William and Misnomer Point. The area was visited by early 19th century sealers operating from neighbouring Clothier Harbour; the feature was surveyed and named by the 1949 Chilean Antarctic Expedition under Captain Leopoldo Fontaine. The cove's midpoint is located at 62°22′15.7″S 59°41′47.9″W. Alfatar Peninsula Robert Island L. L. Ivanov. Antarctica: Livingston Island and Greenwich, Robert and Smith Islands. Scale 1:120000 topographic map. Troyan: Manfred Wörner Foundation, 2009. ISBN 978-954-92032-6-4 SCAR Composite Antarctic Gazetteer

University of Arkansas at Monticello School of Mathematical and Natural Sciences

The School of Mathematical and Natural Sciences is the school of sciences of the University of Arkansas at Monticello. It is located in the Science Center Building on the UAM campus in Arkansas; the School employs 23 faculty and offers Bachelor of Science degrees in four major areas: Biology, Chemistry and Natural Sciences. It has around 176 students enrolled in its minor programs; the School is home to pre-professional programs in: Allied Health, Pre-Dentistry, Pre-Engineering, Pre-Medicine, Pre-Optometry, Pre-Pharmacy. The mission of the School of Mathematical and Natural Sciences is to offer specialization in biology, chemistry and natural science and to provide opportunities for all students to enhance their understanding of science and mathematics. Curricula offered in the School prepare graduates for careers in industry and teaching, for graduate studies, for admission to professional programs including allied health, engineering, medicine and pharmacy; the School of Mathematical and Natural Sciences offers undergraduate programs that lead to the Bachelor of Science degree in four major areas: Biology, Chemistry and Natural Sciences.

The School of Mathematical and Natural Sciences is home to pre-professional programs in: Allied Health, Pre-Dentistry, Pre-Engineering, Pre-Medicine, Pre-Optometry, Pre-Pharmacy. The School of Mathematical and Natural Sciences offers Bachelor of Science Degrees in the following disciplines: Biology - The biology program at UAM includes 6 full-time faculty members. A major and a minor in biology are available. In addition, pre-medicine, pre-dentistry, numerous allied health programs are administered and advised by the biology faculty. Biology majors can choose between different areas of concentration and pre-professional pathways: Standard Biology, Organismal Biology, Biology with Natural Science Minor, Pre-Dentistry, Pre-Medicine. Chemistry - The chemistry program at UAM includes 3 full-time faculty members, 1 faculty member shared with biology, 1 full-time laboratory director. A major and a minor in chemistry are available. In addition, a pre-pharmacy program is advised by the chemistry faculty.

The program has modern chemistry laboratory equipment available for student use including NMR, Fourier transform infrared spectroscopy, ultraviolet-visible spectroscopy, atomic absorption spectroscopy, GC, HPLC. A modest amount of student research is supervised by the faculty. Mathematics - The mathematics program at UAM includes 8 full-time faculty members and one administrator teaching one course per semester. A major and a minor in mathematics are available; the mathematics faculty teaches a limited number of computer science courses. Natural Science - The natural science program at UAM utilizes faculty from the various science disciplines within the School of Mathematics and Natural Sciences. A major and a minor in natural science are available. Pre-Medical - The University of Arkansas-Monticello School of Mathematical and Natural Sciences has an excellent pre-medical program. Our students have been accepted to outstanding medical schools throughout the region; the Medical College Admission Test requires that students be well-versed in biology, chemistry and mathematics.

Students who wish to attend medical school pursue a Bachelor of Science in Biology. The Pre-Medicine Curriculum includes all the requirements for a B. S. in Biology, as well as the standard medical school requirements. Because a great deal of chemistry is required for the B. S. and for medical school, Pre-Med students minor in Chemistry. Outstanding students may wish to pursue a double major in Chemistry. A degree minor in physics is available. UAM M&S Degrees UAM M&S Programs UAM School of Mathematical and Natural Sciences

Serbian Chamber of Commerce

The Chamber of Commerce and Industry of Serbia is independent and responsible non-budget institution, the national association of all Serbian businesses which its tradition and knowledge put in the best interest of its members and the economy of Serbia. To establish Serbia as a country with great investment potential, free market economy and open borders, a country prepared to be competitively integrated into the European mainstream. A century and a half long tradition of the chamber system of Serbia and spread chamber network encompassing sixteen Regional Chamber of Commerce, two Provincial Chambers, Belgrade Chamber of Commerce and Industry and nine representative offices abroad are supporting economy and the business community. Serbian Chamber of Commerce was founded in 1857, it was the first commercial association called " Trade Board ". In 1870 the trade committees were formed in Šabac, Valjevo. In 1910 they founded the Industrial and Workers Association. In 1931 the chambers were recognized as public law organizations and advisory bodies of the state administration.

After the Second World War in 1945 begins with the establishment of branch chambers. In 1962 the reversed branch of commerce were uniform Chamber of Commerce also. In 2001 the effective Reform Act chambers happened; the changes were made to the Law on Chambers of Commerce in 2009. In 2013 came into force the new Law on Chambers of Commerce. Main activities of Serbian Chamber of Commerce are representing the interests of members in front of the state authorities and institutions, carrying out the public powers by the issuance of various documents, improvement of the international economic relations and promotion of the economy both in the country and abroad. Another important activities are in providing business information and consulting services. Business training is included in activities that Serbian Chamber of Commerce is providing, fostering good business practices and business ethics. Courts and Court of Arbitration at the CCIS also; the Assembly is the supreme body of the Chamber of Commerce and Industry of Serbia counting 144 members who are being elected in accordance with four criteria: region, territory and section.

The CCIS Assembly adopts the Statute of the Chamber of Commerce and Industry of Serbia, the Chamber Work Program, the Financial program, the Annual financial report of the Chamber, the Decision on the amount of membership dues and payment deadlines, the Codex and other codes of conducting. The Chamber defines its opinion and gives further directions of functioning to the authorities and bodies of the Chamber in the field of economic development, the economic system and macroeconomic policy and improvement of the international economic relations, etc; the Regulatory Board of the Chamber is a regulatory body of the Chamber that controls the legislation of the Chamber work, the implementation of the Statute and other acts of the Chamber. It controls the Budget of its Professional departments, it counts seven members. They are recognized by the Managing Board; the term of the office of the members of Regulatory Board is up to four years and it may be renewable just once. The Regulatory Board of the Chamber controls the legislation of the Chamber work, the implementation of the Statute and other general acts of the Chamber.

It controls the Budget of all Professional Departments. It counts seven members who are elected from the list of the members of the Chamber and on suggestion of the Managing Board; the term of the office of the members of Regulatory Board is up to four years and it may be renewable just once. The President of the Chamber of Commerce and Industry of Serbia is nominated by the Chamber Assembly from the list of successful businessmen and at the proposal of the Managing Board; the term of the office of the President is up to four years. It may be prolonged just once for another period of up to four years; the President is in charge of his activities to the Chamber Assembly. The President represents the Chamber and is responsible for the legislation of its work and coordinates the cooperation with the National Assembly and the Government of the Republic of Serbia and other authorities and organizations, cooperates with chambers of commerce in Serbia and abroad and with other international and national economic organizations and associations.

The President of the Chamber of Commerce and Industry of Serbia is Željko Sertić. Association of Energy and Energy Mining Association of Construction, Building Material Industry and Housing Association of Chemical and Pharmaceutical Industry and Non-Metal Industry Association of Textile, Garments and Footwear Industry Association of IT Industry Association of Communal Activity Association of Metal Mines and Non-Ferous Metallurgy Association of Creative Industry Association of Metal and Electro Industry Association of Agriculture, food Industry, Tobacco Industry and Water Management Association of Forestry and Wood Processing Industry and Paper Association of Trade Association of Tourism and Hospitality Business Association of Transport and Telecommunications Association of Private Security ICC Eurochambres ABC ASCAME CEFTA BSEC Serbia Investment and Export Promotion Agency Chamber of Commerce and Industry of Serbia Serbian Chamber of Commerce Linkedin