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# Linear programming of basic economic parameters used at reengineering in small

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### Linear programming of basic economic parameters used at reengineering in small

1. 1. INTERNATIONAL JOURNAL OF MANAGEMENT (IJM) International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 – 6510(Online), Volume 4, Issue 2, March- April (2013)ISSN 0976-6502 (Print)ISSN 0976-6510 (Online)Volume 4, Issue 2, March- April (2013), pp. 31-43 IJM© IAEME: www.iaeme.com/ijm.asp ©IAEMEJournal Impact Factor (2013): 6.9071 (Calculated by GISI)www.jifactor.com LINEAR PROGRAMMING OF BASIC ECONOMIC PARAMETERS USED AT REENGINEERING IN SMALL AND MEDIUM ENTERPRISES Prof. Dr Slobodan Stefanović High School of Applied Professional Studies, Vranje, Serbia Prof. Dr Radoje Cvejić Faculty for strategic and operational management Belgrade, Serbia ABSTRACT In economic terms, linear programming is a mathematical technique used for selecting one among more possible economic decisions that will have the greatest efficiency. Most production issues have been solved by a linear programming method, also performed here, and a model of linear programming of economic parameters in re- engineering of small and medium enterprises, for their greater efficiency, is presented. Key words: linear programming, re-engineering, economic parameters, model. 1.0. INTRODUCTION Linear programming is a mathematical method for selecting an optimal solution among larger number of possible solutions. In mathematical terms, linear programming is a mathematical analysis of optimum problem. These are mathematical methods used for seeking the maximum (or minimum) value of a linear function, with previously given limits expressed by a system of linear equations and inequalities. 31
2. 2. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)2.0. A MODEL OF LINEAR PROGRAMMING OF ECONOMIC PARAMETERS OFRE-ENGINEERING Before we consider theoretical basis of linear programming through an example offorming a mathematical model for problems of linear programming of economic parametersof re-engineering. For using linear programming, we shall present the basic groups ofeconomic parameters of re-engineering comprising ratios of production, labor in itsorganization and capital.GROUP 1 PARAMETERS – GENERAL HOLDERS OF ECONOMIC EFFECTS OF RE-ENGINEERING AND ANALYSIS OF NECESSARY ORGANIZATIONAL CHANGES INSMALL AND MEDIUM ENTERPRISES AND HYPOTHESES (parameter X1)GENERAL HOLDERS OF ECONOMIC EFFECTS OF RE-ENGINEERING:∑ UKN 5 pred .troskovi = (NEE NO = NEE NP ) + NEE NP + NEE SP + NEE PR + NEE PP + NEE NSR . (1)i =1Cartesian product of integration rules of computer integrated manufacture CIM: ∑P + ∑T + ∑I + ∑C n n n nR PP → INTCIM i j k l , (2) i =1 i =1 i =1 i =1HYPOTHESES OF A RE-ENGINEERING MODEL AUXILIARY HYPOTHESES:PARAMETERS - NEE FS , NEE KP , NEESK , NEE CP .MAIN HYPOTHESIS:An initial frame for implementation of procedures of logic system reengineering: PHASE I:Establishing initial values of logic performances NEE FS IFAZA , PHASE II: Measuring logicsystem performances NEE FS IIFAZA .Economic parameters for providing functioning of entrepreneurship for implementation of re-engineering NEE KP .Economic parameters for providing functioning of all structures and quality systems in smalland medium enterprises in re-engineering management:NEESK = NEEIM + NEE IS + NEE TO + NEE D + NEE DUR + NEE PPP + NEE DI .Economic parameters for providing competitiveness of a product price on the marketNEE CP created in manufacturing conditions by applying re-engineering:NEE CP = ∑ NEE CP (i = 1...7) . 7 i i =1 32
3. 3. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)GROUP 2 PARAMETERS – FORMING PRICES OF THE PRODUCTS FROM SMALLAND MEDIUM ENTERPRISES THROUGH THE PRODUCTION FACTOR 1. Manufacture costs, i.e. value of goods to be expressed in money TR P , 2. Value of money material used for calculating the value of goods VNM , 3. Size of price measure used as a unit of value measurement CN , 4. Supply and demand ratio PT .GROUP 3 PARAMETERS – NON-ECONOMIC FACTORS VEFGENERAL FINANCIAL PARAMETERS OF A SMALL OR MEDIUM ENTERPRISEFUNCTION, CAUSATIVELY INFLUENCING IMPLEMENTATION OF RE-ENGINEERING 1. Marketing function (R M ) , 2. Scientific research function (R NR ) , 3. Management approach in production planning function R Md| , ( ) 4. Function of financial planning for developing an enterprise (R P ), 5. Function of planning and business control (R PKP ) , 6. Economic – financial function (R EFF ) , 7. Function of connecting incomes with performance (R VZP ) .3.0. COMPREHENSIVE REVIEW OF BASIC ECONOMIC FACTORS INFORMING A RE-ENGINEERING MODEL For forming a re-engineering model in small and medium enterprises in view ofeconomic factors, it is required to include all significant analysis comprising: (1) ANALYSIS OF NECESSARY ORGANIZATIONAL CHANGES IN SMALL AND MEDIUM ENTERPRISES (ANOP) This analysis includes Cartesian product of integration rules of computer integratedmanufacture (CIM) – of an enterprise and given set of components: ∑P + ∑T + ∑I + ∑C n n n n R PP → INTCIM i j k l . i =1 i =1 i =1 i =1 (2) ANALYSIS IN VIEW OF A RESEARCH SUBJECT – HOLDERS OF ECONOMIC EFFECTS OF RE-ENGINEERING (AAPI) Analysis in view of research subject refers primarily to a method of implementationof re-engineering in small and medium enterprises and includes the following costs andsavings comprising the following economic parameters: a parameter NEE NO = NEE NP ,NEE NO - a parameter of economic effect holder referring to new organizational model and itexclusively depends on NEE NP - a parameter of economic effect holder referring to nature ofnew businesses in new organization of small and medium enterprise by applying re-engineering; parameters created by implementation of systematic support to new organizationof small or medium enterprise; /parameter NEE SP - a parameter of economic effect holder 33
4. 4. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)referring to implementation of systematic support; parameter NEE PR - a parameter ofeconomic effect holder referring to implementation of “pilot solution”; parameter NEE PP - aparameter of economic effect holder referring to invested time required for implementation ofplanned changes and application of plan in implementation of re-engineering in phases in anenterprise; parameters being general, but referring to training of employees for new processand new work system with planned changes and application of plan in implementation of re-engineering in phases; /parameter NEE NSR - a parameter of economic effect holder referringto costs due to training of employees for new work system. In view of analysis, total costs∑ UKN 5 Previous .COSTS resulting from application of a research subject, and defined as economici =1parameter holders in implementation of re-engineering, are expressed by adding all theselisted parameters: ∑ UKN 5 Previous. COSTS = (NEE NO = NEE NP ) + NEE NP + NEE SP + NEE PR + NEE PP + NEE NSR . (3) i =1 (3) ANALYSIS OF BASIC HYPOTHESES (AOH) The analysis of basic hypotheses includes following economic parameters of costsresulting from implementation of re-engineering in business activities and staff revitalization,i.e. adjusting organizational structure in terms of ownership restructuring, and defines it asfour economic parameters in defining auxiliary hypotheses, as follows: 1. parameters of financial recovery of small or medium enterprise NEE FS ; this parameter includes 2 phases: PHASE I: Establishing initial values of logic performances NEE FS IPHASE , PHASE II: Measuring logic system performances NEE FS IIPHASE . 2. parameters for providing functioning of entrepreneurship for implementation of re- engineering NEE KP . 3. parameters for providing functioning of all structures and quality systems in small and medium enterprises by implementation of re-engineering NEE SK ; NEE SK = NEE IM + NEE IS + NEE TO + NEE D + NEE DUR + NEE PPP + NEE DI . 4. parameters for providing competitiveness of a product price on the market NEE CP created in manufacturing conditions by applying re-engineering: NEE CP = ∑ NEE CPi (i = 1...7) . 7 i =1 Analyzed economic parameters determine justification and prove the main hypothesisof a re-engineering model, i.e. “By forming a basic model of re-engineering with financialanalysis method – production factors, we can classify all economic parameters activelyinfluencing in a price of finished product being a result of manufacture in small andmedium enterprises”. 34
5. 5. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) (4) ANALYSIS OF FORMING PRICES OF THE PRODUCTS FROM SMALL AND MEDIUM ENTERPRISES THROUGH THE PRODUCTION FACTOR (AFCP) I) Price rate of products from small or medium enterprises It depends on the following most significant economic parameters causatively influencing results of re-engineering, as follows: • manufacture costs, i.e. value of goods to be expressed in money TR P , • value of money material used for calculating the value of goods VNM , • size of price measure used as a unit of value measurement CN , • supply and demand ratio PT • non-economic factors VEF . Depending on a method and conditions for forming product prices, we distinguish thefollowing types of economic factors affecting value of the product price and contributing tomonitoring re-engineering in the field of product price: 1. free market prices – formed by action of supply and demand law onto free competitive market CN ST , 2. monopoly prices – formed and determined by monopoly, i.e. one or few manufacturers that dictate the offer, and accordingly a price itself CN M , 3. administrative prices – prices determined by the state CN A , 4. mixed prices – prices formed under influence of market and administrative means CN MŠ . II) Production function (P) , Production function is different from technology, being a technological efficiency, anddefines the maximum of production range, resulting from every possible combination of productionfactors. P = f (x, y, z.....) ,The simplest is possible, to express production function by Domar’s method: K P= , (4) kWalrase – Leontiev production function includes several factors. According to this function,production sector product is: X ij Pj = , (5) a ijDouglas production function, expressed in general form as: P = C Ra Kb, (6) 35
6. 6. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)Therefore, in general case: P1 = C (p X )x Yy Zz , (7) P1 = p x C Xx Yy Zz , (8) P1 = p x P. (9)II.1. Production possibility frontier ( G Pr MII.2. Law of diminishing returns ZO PrII.3. Marginal productivity of production factorsII. 3.1. Total, mean and marginal product (marginal analysis)Mean product is obtained by dividing total product of a factor and the amount of consumption ofthat factor, as in formula: U prxi Pprxi = . (10) xiMarginal product is increase in total product at unit change in the amount of consumption of afactor: U Prxi Uprxi 1 ∆U Prx G Prx = = . (11) xi xi 1 ∆xII. 3.2. Total, mean and marginal costsTotal costs UTr are neither homogeneous nor increase at all production levels proportionallywith the increase of the output. Total production costs are divided into fixed UFTr ; variableUVTr costs, and therefore total production costs may be expressed by the formula: UTr = UFTr + UVTr . (12)Marginal costs are expressed with the following pattern: GTr = UVTr . UVTrIf there are no unit changes in the production range: GTr = , Q – production range. QThe enterprise will engage all production factors until there is equalization between marginalphysical product at last money unit spent for each production factor: CFPx CFPy CPFz = = .... = . (13) Cx Cy Cz 36
7. 7. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) III) Demand for production factorsMarginal revenue is a change in total enterprise revenues, when production range changes by unit. Onthis basis, we have: UPd - VGP (marginal revenue of factors) = , R UTr - GPd (marginal revenue) = , R UTr - GTr (marginal cost) = . Q IV) Production factor offer V) Production factor market VI) Production factor procurement and product sale on the perfectly competitive market VII) Perfect competitiveness in product factor procurement, but monopoly in product sales VIII) Bilateral monopoly IX) Price – production factor incomes (gain, rent, interest and profit)4.0. AN EXAMPLE OF THE LINEAR PROGRAMMING ECONOMIC EFFECTS OF RE-ENGINEERING BY USING THE PROPOSED MODEL Let us suppose that a small or medium enterprise manufactures two products, P1 and P2 . Formanufacturing these products, it is required to understand general economic parameters of re-engineering with using group parameters M 1 , M 2 and M 3 for their production. For manufacturingone unit of the product P1 , it takes 2 hours for machine work with using general economicparameters of re-engineering M 1 , e.g. 1 hour of machine work with using general economicparameters of re-engineering M 2 and e.g. 2 hours of machine work M 3 with using generaleconomic parameters of re-engineering. Machine capacities are expressed in available hours of eachmachine in observed time period and they amount: 100 hours for machine 1, 120 hours for machine 2and 120 hours for machine 3. A small or medium enterprise realizes income of 6 dinars per productunit P1 , and 4 dinars per product unit P2 . All these data are shown in Table 1. The problem is the following: which quantities of P1 and P2 products should bemanufactured in small and medium enterprises by using economic parameters of re-engineering torealize maximum income by using economic parameters of an enterprise in re-engineering function atgiven limiting conditions (capacities). From the problem set like this, we can see that quantities of P1and P2 products that should be manufactured according to optimal production program by usingeconomic parameters of re-engineering are unknown. We shall mark general economic parameters ofre-engineering and parameters of analysis of necessary organizational changes affecting manufactureof a product P1 , produced in a small or medium enterprise with X 1 , and the amount of P2 productproduced by using the same economic parameters and analysis as in previous case with X 2 , andform a mathematical model for this problem.The income that will be realized on P1 product will be 6X 1 , and on P2 product 4 X 2 , for a totalZ0 = 6X1 + 4X 2,where z 0 is total income, and entire formula will be called a criteria function, or optimalitycriterion of economic parameters of reengineering. 37
8. 8. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) According to the defined problem, we seek for the maximum value of total revenue, sowe have the following criterion function:(max); z0 = 6 x1 + 4 x2 .In a similar way, we shall formulate limiting factors, for each group of parameters individually.It takes 2 hours for the machine 1 to produce one unit of a product P1 with using abovementioned economic parameters of re-engineering, i.e. 2 x1 hours to produce total amount of thisproduct. This machine also produces the product P2 , and it takes 1 ⋅ x 2 hours for a machine 1 toproduce x 2 units of this product. Total time for manufacturing whole quantity of products P1 and P2 amounts 2 x1 + x 2 . Certainly, total used hours for the machine 1 for manufacturing products P1 and P2 cannot be more than total available amount being 100 hours for the observed timeperiod. In that way we get an inequality:2 x1 + x2 ≤ 100.In the similar way, we obtain the corresponding inequalities through which capacities ofmachines 2 and 3 are expressed:x1 + 3x 2 ≤ 120,2 x1 +2 x 2 ≤ 120.In its nature, production range cannot be negative, and the previous conditions should becomplemented by a condition that x1 and x 2 variables cannot be negative, i.e. x1 ≥ 0, x 2 ≥ 0. In this way, we obtained a mathematical model from certain expressions for previouslyformulated problem of determining the amount of products produced in small or mediumenterprises by using economic effects of re-engineering. It consists of a function for optimalitycriterion of economic parameters of re-engineering.z 0 = 6 x1 + 4 x2 ,whose maximum value should be find with the following limitation system:2 x1 + x 2 ≤ 100, x1 + 3x 2 ≤ 120,   (1,4)2 x1 + 2 x 2 ≤ 120,x1 ≥ 0, x 2 ≥ 0.  NOTE 1: Lines with arrows indicate connection between economic parameters of re-engineering, i.e. that they affect all products and their production values and revenues equally.NOTE 2: For smooth operation of technical systems (machines) M 1 , M 2 and M 3 , allproduction conditions with limiting factor systems have been met: a) production issues, b)transport issues, c) location issues, d) distribution issues, e) establishing plans for foreign trade, f)various structural problems solved. Our task is to define such values for variables x1 and x 2 that will satisfy the system ofinequalities and ensure that criterion function reaches its maximum value.We simplified the problem because there are only two variables, and therefore it can be solvedgraphically. This method of solving enables presentation of the problem essence, and before westart its analytical solving. The graphical method for solving linear problems may be appliedonly if a problem has no more than two variables. 38
9. 9. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 – 6510(Online), Volume 4, Issue 2, March- April (2013) Table 1. Parameters influencing on optimality criterion of economic parameters of reengineering Time required for producing a Capacity of unit of a product by using amounts in PARAMETER economic parameters of re- hours by engineering using P1 - product P2 - product capacities (P1 = ( f ( M1, M 2 , M P2 = f ( M1 , M 2 , MM 1 = X 1 = X I 1 + X I 2. - GROUPE M1 PARAMETERS: GENERALHOLDERS OF ECONOMIC EFFECTS OF RE-ENGINEERING ANDANALYSIS OF NECESSARY ORGANIZATIONAL CHANGES IN SMALL ANDMEDIUM ENTERPRISES AND HYPOTHES 1. GENERAL HOLDERS OF ECONOMIC EFFECTS OF RE- ENGINEERING: 5 X 11 X 12 X 13X I 1 = ∑ UKN pred .troskovi = ( NEE NO = NEE NP )+ NEE NP + NEE SP i =1 2 1 100 X 14 X 15 X 16+ NEE PR + NEE PP + NEE NSR and Cartesian product of integration rulesof computer integrated manufacture CIM:  nX 18 X 1.10 X 1.11  X 17  n X 19 n n RPP → INTCIM ⋅  ∑ Pi + ∑ T j + ∑ I k + ∑ Cl .  i =1 i =1 i =1 i =1    X 1.12 X 1.13 X 1.14HYPOTHESES PARAMETERS - X I 2 , NEE FS , NEE KP , NEE SK k.M 2 = X 2 = X II 1 + X II 2. GROUP M2 PARAMETERS – FORMINGPRICES OF PRODUCTS PRODUCED IN SMALL AND MEDIUMENTERPRISES THROUGH PRODUCTION FACTOR and Production factoroffer, Production factor market, Production factor procurement and product saleson the perfectly competitive market, Perfectly competitiveness in procurement ofproduction factors, Monopoly in product sales, Bilateral monopoly, Price –production factors incomes (gain, rent, interest and profit)PARAMETRI SU: TR P , VNM , CN , PT , U prxiP = f ( x, y, z.....) , Ppr = ,, xi xi U Pr xi Uprxi −1 ∆U Prx UTr = UFTr + UVTr , VGP (marginal revenue ofG Prx = = , 1 3 120 xi − xi −1 ∆xfactors) = Uod/R GPd (marginal revenue) = Utr/R, Marginal cost = Utr/Q.M 3 = X 3 = X III 1 + X III 2. GROUP M3 PARAMETERS – NON-ECONOMIC FACTORS VEFGENERAL FINANCIAL PARAMETERS OF A SMALL OR MEDIUM 2 2 120ENTERPRISE FUNCTION, CAUSATIVELY INFLUENCINGIMPLEMENTATION OF RE-ENGINEERING:(RM ) , (R NR ) , (RMd | ) , (RP ) , (RPKP ) , (REFF ) .TOTAL REVENUE PER PRODUCT UNIT 6 4 - 39
10. 10. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) The problem is solved by presenting graphically all inequalities from the system oflimitation, in Descartes coordinate Oxy system. Since variables x1 and x 2 cannot be negative, we use only the first quadrant forgraphical presentation of the limitation system and present each inequality separately.Let us present the first inequality related to the machine 1. By using common graphicpresentation, we first draw equation 2 x1 + x 2 = 100. This is the line which intersects withaxis x1 in a point M 1 (50.0), and axis x 2 in M ,1 (0.100). The line that goes through thesetwo points, forms a triangle with tips O, M 1 , M ,1 with axes x1 and x 2 (in Figure 1). Alltriangle points meets the first limitation and meet the requirement of non-negativity ofvariables. In the same way, we can set the other limitation through the appropriate equations.The second limitation intersects with axis x1 in point M 2 (120.0) and with axis x 2 inpoint M , 2 (0.40) thus forming a triangle OM 2 M , 2 . Finally, the third limitation intersectsthe first axis in point M 3 (60.0), and the second axis in point M , 3 (0.60) and forms atriangle OM 3 M , 3 . The solution to the problem has to meet every limitation individually, but also alllimitations taken together. Therefore, all limitations of the system (1,4) form commonarea OM 1CM , 2 , being patterned in Figure 1. Each point of common area meets setlimitations, and therefore are the set of the possible solutions. It is required to determinethe solution from the set of possible solutions, that will ensure that the criterion function(1,1) will reach its maximum value. It can be easily calculated that the extreme points M 1 , C and M , 2 of the common area correspond with the following criterion functions:M 1 : x1 =50, x 2 = 0, z 0 = 300,B : x1 =40, x 2 = 20, z 0 = 320,C : x1 =30, x 2 = 30, z 0 = 300, ,M 2 : x1 =0, x 2 = 40, z 0 = 160. Point B, with coordinates x1 = 40 and x 2 = 20, meets the limitation system (1,4)and ensures maximum value of criterion function (1.4.), and therefore it is the optimalsolution to the problem. It should be said that it is not necessary to determine the values of the criterionfunction for all extreme points to select the optimal solution. This can be achieved bygraphical presentation of the criterion function z 0 and its parallel movements. Therefore,the maximum value of the criterion function will be reached when its graph is at thefarthest point from the coordinate start while going through at least one point of thecommon area. 40
11. 11. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) X2 M 1 (0,100) M 3 (0,60) M 2 (0,30) B (40,20) X 2 =20 0 40 50 60 100 120 X1 X 1 =40 X 1 +3X 2 =120 2X 1 +X 2 =100 2X 1 +2X 2 =120 Figure 1. The area of optimal economic parameters of reengineering - the area of O50BM , 2 pointsIn the end, we can conclude that optimal solution, x1 = 40 and x 2 = 20 shows that a small ormedium enterprise should produce 40 units of the product P 1 and 20 units of the product P2to realize the maximum possible revenue under given conditions of 320 dinars with using alleconomic parameters of re-engineering. Every other production program will yield lessincome. This method can be successfully used as a basic method in programming theproduction in small and medium enterprises by using all economic parameters of re-engineering.5.0. CONCLUSION Optimality criterion function of economic parameters of re-engineering my beanalytically determined by using common area with common expression:A: x1 = 5 ⋅ n, x 2 = 0 ⋅ n, z 0 = 6 ⋅ n ;B: x1 = 4 ⋅ n, x 2 = 2 ⋅ n, z 0 = 6,4 ⋅ n ;C: x1 = 3 ⋅ n, x 2 = 3 ⋅ n, z 0 = 6 ⋅ n ;D: x1 = 0 ⋅ n, x 2 = 4 ⋅ n, z 0 = 3,2 ⋅ n ;This implies that by approximation, the mean value of the optimality criterion function forthe presented case is: 6 + 6,4 + 6 + 3,2 x1 = (2 z + 1) ⋅ n, x 2 = (2 z − 1) ⋅ n, z 0 = ⋅ n = 5,4 ⋅ n ; which applies for 4 z = 0,1,2,3.In Descartes coordinate system, this curve may be presented based on values entered in Table2 (Figure 2): 41
12. 12. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) Table 2. Shadow Box field representing optimal area of economic parameters of reengineering Point M1 B C M ,2 x1 50 40 30 0 x2 20 20 30 40 z0 300 320 300 160Based on this, we can conclude that general expressions of optimality criterion are: x1 = (2 z + 1) ⋅ n, z = 0,1,2,3. (14) x 2 = (2 z − 1) ⋅ n, z = 0,1,2,3. (15) z0 = i ⋅ n , (16) where i depends on optimality criterion of economic parameters of re-engineering. X2 Tacka M1 B C M2 X1 50 40 30 0 40 X2 20 20 30 40 30 Z0 300 320 300 160 M2 20 30 40 50 C X1 160 M1 B 300 320 Z0Figure 2. Optimality criterion function of linear programming of economic parameters of programming – spatial curve 42