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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Problem1.3-1 Application：Logistical planning of shipments Organization:Federal Express Federal Express is the world’s largest express transportation company‚providing fast and reliable services for important documents ‚packages‚and freight.It’s success was gave the credit to the use of Operations Research. Operations Research modeling was a way of life for Federal Express‚there were three famous Model planning system‚one is origin-destination flow model which worked out a 26-city system
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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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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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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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Managerial Decision Modeling w/ Spreadsheets‚ 3e (Balakrishnan/Render/Stair) Chapter 4 Linear Programming Sensitivity Analysis 4.1 Chapter Questions 1) Surplus is typically associated with which type of constraints? A) ≤ B) ≥ C) = D) ≠ E) ± Answer: B Page Ref: 124 Topic: Sensitivity Analysis Using Graphs Difficulty: Easy 2) Assume that the shadow price of a non-binding "≤" constraint is 5. This implies that: A) if the right-hand side value of the constraint increases by 1 unit‚ the objective
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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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Chapter 2 An Introduction to Linear Programming 18. a. Max 4A + 1B + 0S1 + 0S2 + 0S3 s.t. 10A + 2B + 1S1 = 30 3A + 2B + 1S2 = 12 2A + 2B + 1S3 = 10 A‚ B‚ S1‚ S2‚ S3 0 b. c. S1 = 0‚ S2 = 0‚ S3 = 4/7 23. a. Let E = number of units of the EZ-Rider produced L = number of units of the Lady-Sport produced Max 2400E + 1800L s.t. 6E + 3L 2100 Engine time L 280 Lady-Sport maximum
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