Graphical and Simplex Methods of Linear Programming The graphical method is the more popular method to use because they are easy to use and understand. Working with only a few variables at a time they allow operations managers to compare projected demand to existing capacity. The graphical method is a trial and error approach that can be easily done by a manager or even a clerical staff. Since it is trial and error though‚ it does not necessarily generate the optimal plan. One downside of this
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Operations Management II Introduction to Operations Research Operations Research (OR) Definition Operations Research is the representation of real world systems by mathematical models together with the use of quantitative methods (Algorithms) for solving such models‚ with a view of optimising. - (J.E Beasley) “The attack of modern science on complex problems arising in the direction and management of large systems of men‚ machines‚ materials and money in industry‚ business‚ government
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SENSITIVITY ANALYSIS The solution obtained by simplex or graphical method of LP is based on deterministic assumptions i.e. we assume complete certainty in the data and the relationships of a problem namely prices are fixed‚ resources known‚ time needed to produce a unit exactly etc. However in the real world‚ conditions are seldom static i.e. they are dynamic. How can such discrepancy be handled? For example if a firm realizes that profit per unit is not Rs 5 as estimated but instead closer
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Section two — facility location Competitive imperatives impacting on location decision Location decision and location factors Service versus industrial locations Location methods for industrial and service companies Factor rating methods Linear programming Transportation method Further explorations on transportation method Centroid method (Centre of gravity method) 7 7 7 10 10 11 13 16 22 23 Section three — operations facility strategies Basic types of layout for manufacturing Some layout
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what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer. To do this we have used Linear Programming (LP) – a technique specifically designed to help managers make decisions relative to the allocation of resources. In this case‚ C-30 = ‚ C-92 = ‚ D-21 = ‚ and E-11 = . The constraints for this case were translated into linear equations (i.e. inequalities) to mathematically express their meaning. The first constraint that C-11 must constitute for at least
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are the most popular food items among fans and so these are the items she would sell. If Julia clears at least $1‚000 in profit for each game after paying all her expenses‚ she believes it will be worth leasing the booth. A. Formulate a linear programming model for this case. Decision Variables Representing “x1” as pizza slices‚ “x2” as hot dogs‚ and “x3” as barbeque sandwich The Objective Function The objective is to maximize total profit. Profit is calculated for each variable by
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Assignment #3 The following variables will be used: X1 = Slices of Pizza X2 = Hot Dogs X3 = BBQ Sandwiches The objective is to maximize profit. maximize Z= 0 .75X1+1.05X2+1.35X3 Subject to: 0.75X1+1.05X2+1.35X3≤1‚500(Budget) 24X1+16X2+25X3≤55‚296in2 (Oven space) X1≥X2+X3 X2X3≥2.0 X1‚ X2‚ X3≥0 Julia’s Food Booth Food items: Pizza Hot Dogs Barbecue Profit per item: 0.75 1.05 1.35 Constraints: Available Usage Left over Budget ($) 0.75 0.45 0.90 1‚500
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Problem 4. (25 Points) Solve the following problem graphically (Please be neat). Draw the polytope on the x-y coordinate system (can be done either by hand or computer). Show all intersection of the polytope and identify the point (x‚y coordinate) where the objective function is maximized and provide that value. Maximize Z = 3x1 + 2x2 Subject to: 1x1 + 1x2 ≤ 10 8x1 + 1x2 ≤ 24 and x1‚ x2 ≥ 0 Solution : Point (a) is the origin (0‚0) where Z(a) = 3*0 + 2*0 = 0 Point (b) is the
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~61E LINEAR ALGEBRA QUESTION ı The blanks below will be filled by students. i Name: Surname: Signature: 22 MAY 2013 FINAL i Electronic Group Number: \ List Number: Post( e-mail) address: For the solution of this question (Except the score) Score Student Number: please use only the front face and if necessary the back face of this page. [ı2 pts] (a) Find the transition matrix from the ordered basis [(ı‚ ı‚ ı)T‚ (ı‚ 0‚ O)T‚ (0‚2‚ ı)T] of R3 to the ordered
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Define and contrast Structured Programming against Object-Oriented Programming. Be sure to address pros and cons for each method. Use charts as necessary to supplement written research. Edson Cazeau COP 3530 PBSC Fall 2012 Dr. Rolando Object Oriented Programming (OOP) and Structured Programming are two programming paradigms. A programming paradigm is a fundamental style of computer programming. Programming paradigms differ in how each element of the programs is represented and how steps are
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