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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Julia’s Food Booth Case Problem MAT 540- Quantitative Methods February 23‚ 2013 (A) Formulate and solve an L.P. model for this case. The following variables were 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 (B) Evaluate the prospect of borrowing money before the first
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UNIVERSITY OF WATERLOO CO370/CM443: Deterministic OR Models Midterm Examination – FALL TERM 2011 Thursday‚ October 20‚ 2011‚ 7-9 PM (conflict time 4:45-6:45 PM) CLOSED BOOK Surname: First Name: Signature: ID#: INSTRUCTIONS: 1. Write your name and Student ID# in the blanks above. 2. There are five questions. Some questions may be longer or more difficult than others. Read all the questions first and budget your time appropriately for each question. 3. Answer each question in your solution booklet. Problem
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A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Let‚ X1 =No. of pizza slices‚ X2 =No. of hot dogs‚ X3 = No. of barbeque sandwiches * Objective function co-efficient: The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price. For Pizza slice‚ Cost/slice=$4.5/6=$0.75 | X1 | X2 | X3 | SP | $1.50 | $1.60 | $2.25 | -Cost | 0.75 | $0.50 | $1.00 |
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TRUE/FALSE 10.1 The Avis car rental company successfully used the transportation method to move its inventory of cars efficiently. ANSWER: TRUE 10.2 Transportation and assignment problems are really linear programming techniques called network flow problems. ANSWER: TRUE 10.3 A typical transportation problem may ask the question‚ “How many of X should be shipped to point E from source A?” ANSWER: TRUE 10.4 The objective of a transportation problem solution
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categories of modeling techniques includes optimization techniques? Prescriptive models What is the goal in optimization? Find the decision variable values that result in the best objective function and satisfy all constraints. The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to: 2
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APPLIED OPERATIONAL RESEARCH FOR MANAGEMENT NOTES 1 ANNA UNIVERSITY CHENNAI UNIT I INTRODUCTION TO LINEAR PROGRAMMING (LP) INTRODUCTION Operations Research (OR) (a term coined by McClosky and Trefthen in 1940) was a technique that evolved during World War II to effectively use the limited military resources and yet achieve the best possible results in military operations. In essence you can state that OR is a technique that helps achieve best (optimum) results under the given set of limited
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