Formulation of the LPP Suppose Julia stock X1 numbers of pizza slices‚ X2 numbers of hot dogs and X2 numbers of sandwiches. Constraints: 1. On the oven space: Space available = 3 x 4 x 16 = 192 sq. feet = 192 x 12 x 12 =27648 sq. inches The oven will be refilled during half time. Thus total space available = 27648 x 2 = 55296 Space required for pizza = 14 x 14 = 196 sq. inches Space required for pizza slice = 196/ 8 = 24.5 sq. inches Total Space required: 24.5 X1 + 16 X2
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Introduction Julia Robertson‚ a senior at Tech‚ explores various options to support her final year at school and weighs the option of hiring a food booth outside the institute for football games as she knows from her personal experience that during the games‚ people eat lot of food. Facts/Market survey: Before arriving at the final decision‚ she does some market survey and gathers the following information. Hiring cost of booth will be $1000 per game. She would be able to sell only food items from
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Julia’s Food Booth Julia Robertson is a senior at Tech‚ and she’s investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game‚ and Julia knows‚ from attending the games herself‚ that everyone eats a lot of food. She has to pay $1‚000 per game for a booth‚ and the booths are not very large. Vendors can sell either food or drinks on Tech property‚ but not both. Only the Tech
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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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Sandwiches p‚H‚B >= 0 . si>= 0 Based on QM for windows l solution the optimum solution: Pizza (p) = 1250; Hotdogs(H) = 1250 and Barbecue sandwiches (B) = 0 Maximum value of Z = $2250 Julia should stock 1250 slices of pizza‚ 1250 hot dogs and no barbecue sandwiches. Maximum Profit = $2250. |Maximum Profit
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(A) Formulate and solve an L.P. model for this case Variable Food Cooking Area x1 Pizza Slice 24in sq x2 Hot Dogs 16in sq x3 BBQ Sandwiches 25in sq *The oven space required for a pizza slice is calculated by dividing the total area arequired for a whole pizza by the number of slices in a pizza 14 x 14 = 196 in2‚ by 8‚ or approximately 24 in2 per slice. The total space available is the dimension of a shelf‚ 36 in. x 48 in. = 1‚728 in2‚ multiplied by 16 shelves‚ 27‚648 in2‚ which is multiplied
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Julia’s Food Booth Strayer University Quantitative Methods – MAT 540/ Spring 2012 Dr. Buddy Bruner May 19‚ 2012 A) Formulate and solve an L.P. model for this case. [pic] [pic] B) Evaluate the prospect of borrowing money before the first game. After observing the ranging chart calculations indicate that the upper bound in the budget is equal to 1638.4. The original value of the budget
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A. Julia Robertson is considering renting a food booth at her school. She is seeking ways to finance her last year and thought that a food booth outside her school’s stadium would be ideal. Her goal is to earn the most money possible thereby increasing her earnings. In this case problem‚ she decided to sell pizza‚ hotdogs and BBQ sandwiches. The following LP model illustrates the maximum net profit and constraints that will determine whether or not to least the booth. Z = $ .75(X1) + $1.05(X2)
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personalize their case study using their own words/thoughts/style‚ this example is provided as a simple template just to get you started. Your actual Course Professor may provide other guidance‚ too.) Week 7‚ Assignment 3 Quantitative Methods - MAT540 Case Analysis Paper Julia’s Food Booth Chapter 3‚ page 109 Student Name Date Professor ____________________ Strayer University Parameters/Background The case study involving Julia’s food booth …. (provide background
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Julia’s Food Booth A) Formulate and solve an L.P. model: Variables: x1 – Pizza Slices x2 – Hot Dogs x3 – Barbeque Sandwiches Subject to: $0.75x1 + $0.45x2 + $0.90x3 ≤ $1‚500 24x1 + 16x2 + 25x3 ≤ 55‚296 in2 of oven space x1 ≥ x2 + x3 (changed to –x1 + x2 + x3 ≤ 0 for constraint) x2/x3 ≥ 2 (changed to –x2 +2x3 ≤ 0 for constraint) x1‚ x2‚ x3 ≥ 0 Solution: Variable | Status | Value | X1 | Basic | 1250 | X2 | Basic | 1250 | X3 | NONBasic | 0 |
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