Submitted By Freshwinterstorm

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Words 512

Pages 3

Source: www.brainmass.com

Problem Statement

Julia 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 athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.

Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.

Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game – 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 in2 of space, whereas a barbecue sandwich takes up about 25 in2. She plans to sell a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue sandwich for $2.25. She has $1,500…...

...Running head: JULIA’S FOOD BOOTH 1 Case Study Julia’s Food Booth Susan Dawson Strayer University JULIA’S FOOD BOOTH 2 Case Study: Julia’s Food Booth In this case study, we are asked to determine if Julia Robertson, a senior at Tech, should finance her final year at Tech in part by opening a food booth outside the stadium at home football games. We are also asked to determine if she should borrow more money, hire preparation assistance and what could go wrong. Julia is considering opening a food booth outside the stadium at six (6) home football games at a booth rental charge of $1,000.00 per game. Due to existing regulations, she knows she can only sell food or drinks, not both. She has determined the most popular food items are slices of pizza, hot dogs and barbecue sandwiches and that most food sales occur during the hour before the game and during half-time. She has been able to secure a deal with a pizza delivery company to deliver 14” pizzas, 8 slices each, for $6.00 and, because of demand, she must prepare the other food in advance and keep it warm ahead of sales. She found that she can rent a warming oven with 16 shelves, each 3’ x 4’, for a seasonal cost of $600.00 or $100.00 per game. Julia has $1,500.00 available to purchase food for the first game. Thereafter...

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...Assignment #3: Case Problem “Julia’s Food Booth” La-Tia Jackson MAT 540 Dr. Albert Yin May 26, 2013 1. Formulate and solve an L.P. model for this case. There are three products or variables in this problem that we must consider for purchase. X1 = number of pizza slices Julia should purchase X2 = number of hotdogs Julia should purchase X3 = number of barbecue sandwiches Julia should purchase. Julia decided to have a food booth in order to make some money. Her goal is to maximize the profit that she can get from selling the hotdogs, pizza, and barbeque sandwiches that she plans on selling. The first thing to do is find the profit that Julia will make per Item. To find that per Item price, the cost of the item will be subtracted from the selling price. Pizza: Julia can buy a pizza that contains 8 slices for $6. That means each slice of pizza will cost her $0.75. She plans to sell each piece for 1.50. $1.50-$0.75= $0.75 profit Hot dog: $1.50 - $0.45 = $1.05 profit Barbecue Sandwiches: $2.25 - $0.90 = $1.35 profit The objective function can now be written since we have found the potential profit of each food item. The objective of this function is to maximize Z (profit). Z= $0.75x1 + $1.05x2 + $1.35X3 Budget is the one thing that has to be taken into consideration. Julia has $1,500 on hand to purchase and prepare food for the first home game. A constraint must be formed for the budget. Cost of each item and money available is what is known, so it is easy to form......

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...Assignment 3: Julia’s Food Booth Case Problem Marie O. Huddleston MAT 540 – Quantitative Methods December 4, 2013 Dr. Bashir M. Dweik A) Formulate and solve a L.P. model for Julia’s Food Booth. Variables: X1 = pizza slices X2 = hot dogs X3 = barbeque sandwiches. Maximize Z = ($0.75 X1) + ($1.05 X2) + ($1.35 X3) Subject to: ($0.75 X1) + ($0.45 X2) + ($.90 X3) <= $1,500 (24 X1) + (16 X2) + (25 X3) <= 55,296 inches squared oven space X1 >= X2 + X3 (X2/X3) >= 2.0 X1, X2, X3 >=0 Solution: X1 = 1250 pizza slices X2 = 1250 hot dogs X3 = 0 barbeque sandwiches Z = $2,250 Julia will generate revenues of $2,250 for her first game. the leasing of the booth will cost her $1,000/game, so she is left with $1,250. The cost of leasing the warming oven is 600 for 6 games, which comes to $100/game. She will make a profit of $1,150 for her first game. Also see Excel Spreadsheet file tabs 1 & 2 B) Evaluate the prospect of borrowing money before the first game. Yes, she would increase her profit if she borrowed more money. The shadow price, or dual value, is $1.50 for each additional dollar she earns. The upper limit given in the model is $1,658.88, which means she can only borrow $158.88 giving her an additional profit of $238.32. C) Evaluate the prospect of paying a friend $100/game to assist. Yes, I think Julia should hire her friend for $100 per game. In order for Julia to prepare the hot dogs......

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...The three products/variables in this problem that must be considered for purchase are: x1: Pizza Slices x2: Hot Dogs x3: Barbeque Sandwiches The objective is for Julia to maximize profits. Julia’s goal is to earn a profit of at least $1,000.00 after each game. Profit = Sell – Cost Profit Function: Z = 0.75(X1) + 1.05(X2) + 1.35(X3) Constraints and Cost: The maximum amount of funds available for purchase is $1500.00 Cost per pizza slice = $0.75 because Julia purchases each pizza for $6.00 and there are 8 slices per pizza. Cost per hot dog = $0.45 Cost per sandwich = $0.90 LPP Model: Maximize Profit: Z= $0.75x1 + $0.45x2 + $0.90x3 < $1,500 Subject to 24x1 + 16x2 + 25x3 < 55,296 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 Solve the LPM: Pizza(X1) = 1,250; Hotdogs(X2) = 1,250 and Barbecue sandwiches(X3) = 0 Maximum value of Z = $2,250 It would be in Julia’s best interest to stock 1,250 slices of pizza, 1, 250 hot dogs and no barbecue sandwiches as it will yield the maximum profit of $2,250.00 (B) Evaluate the prospect of borrowing money before the first game. I do assert that Julia should borrow money from her friend to increase her profits. The shadow price is $1.50 for each additional dollar Julia earns. The upper limit in the model that is given is $1,658.88. This means that Julia can borrow $158.88 from her friend, which will help her......

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...Assignment #3: Case Problem "Julia's Food Booth" Complete the "Julia's Food Booth" case problem on page 109 of the text. Address each of the issues A - D according the instructions given. (A) Formulate and solve an L.P. model for this case. See Excel worksheet. (B) Evaluate the prospect of borrowing money before the first game. I would suggest that Julia consider borrowing money before the first game to open up her food booth. According to the first constraint, she is subject to a $1,500 budget with a potential to make a profit of $2,250 if she were to sell all her pizza and hot dogs. This result yields a profit of $750 or 50%. Even if no sales were made, the potential is high, considering the opportunity. Plus, I am sure that a small initial investment is not detrimental to her personal funds, to where if things did not go as planned, she could recover the funds. (C) Evaluate the prospect of paying a friend $100/game to assist. I would suggest that Julia consult a friend for $100/game to assist in her food booth. After running a break-even analysis (see Excel), holding all things constant, where she only sells pizza and hot dogs, she would have to sell 67 slices of pizza and 48 hotdogs to break-even after paying her friend $100. This does not seem too farfetched, considering her maximum sales, given these constraints, is 1,250 slices of pizza and 1,250 hot dogs, only about 5% and 4% of maximum sales, respectively. On top of that, Julia may need the help to......

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...this problem? b) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining? c) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining? d) Discuss: Slack (if any); shadow price, and sensitivity analysis results using the program of your choice. Click below link for Answer (I have all problem assignment contact me on chat) http://workbank247.com/q/mat-540-week-8-assignment-1-linear-programming-cas/4572 http://workbank247.com/q/mat-540-week-8-assignment-1-linear-programming-cas/4572 MAT540 Week 8 Assignment Assignment #1: Case Problem "Julia's Food Booth" Complete the "Julia's Food Booth" case problem on page 109 of the text. Address each of the issues A - D according the instructions given. (A) Formulate and solve an L.P. model for this case. (B) Evaluate the prospect of borrowing money before the first game. (C) Evaluate the prospect of paying a friend $100/game to assist. (D) Analyze the impact of uncertainties on the model. Write up. Your write up should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up......

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...Julia 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 athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell. Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time. Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game – 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each......

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...Case 3 - Julia's Food Booth | | | | | | | | | | | | | | | | | |Constraints: | | | |Available |Usage |Left over | | |Budget ($) |0.75 |0.45 |0.90 | 1,500 | 1,500.00 |0 | | |Oven space (sq. in.) |24 |16 |25 | 55,296 | 50,000.00 |5296 | | |Demand |1 |-1 |-1 |0 | - |0 | | |Demand |0 |1 |-2 |0 | 1,250.00 |-1250 | | | | | | | | | | | |Adjustable Cells | | | | | | | | | |Final |Reduced |Objective |Allowable |Allowable | | |Cell |Name |Value |Cost |Coefficient |Increase |Decrease ...

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...Case Problem” Julia’s Food Booth” Julia’s objective is to maximize total profit; the total profit is the summary of the individual profits gained from each pizza slice, hot dog, and barbeque sandwich. I am going to estimate the profit for each item as difference between total revenue and total cost of the item. Total revenue Total cost Profit Pizza slice $1.50 $6/8 slices = $0.75 $0.75 Hot dog $1.50 $0.45 $1.05 Barbeque sandwich $2.25 $0.90 $1.35 x1 - number of pizza slices x2 - number of hot dogs x3 - number of barbeque sandwiches The profit function: maximize Z = $0.75* x1 + $1.05 * x2 + $1.35 * x3 There Z = total profit per game. The oven size constraint is formulated as 16 shelves 3*4 feet each which will be filled twice for each game, so the maximum possible size of the stove is: (((12*3)*(12*4))*16)*2 = 55,296 square inches. Estimate for each item in regards to the space: Pizza slice (14*14)/8 = 24.5 square inches (keeping in mind that she will keep whole pizza warm) Hot dog ...

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...Julia's Food Booth Part A (Formulate) | | | | | Step 1: | Define the decision variables: | | | | | | x1 | = | How many hot dogs to produce to maximize profit | | | x2 | = | How many BBQ Sandwiches to produce to maximize profit | | x3 | = | How many Cheese Pizza slices to sell to maximize profit | | | | | | | | | | | Step 2: | Define the objective function. | | | | | | Maximize the profits of Julia's booth. | | | | | | | | | | | | | | | | | | Cost | Selling Price | Profit | | | | | Profit of Pizza = | $ 0.75 | $ 1.50 | $ 0.75 | | | | | Profit of BBQ = | $ 0.90 | $ 2.25 | $ 1.35 | | | | | Profit of Hot Dog = | $ 0.45 | $ 1.50 | $ 1.05 | | | | | | | | | | | | | | Maximize Z = | $1.05x1 | + | $1.35x2 | + | $.75x3 | | | | | | | | | | | Step 3: | Define the constraints: | | | | | | Size of the shelves in the warming oven (space is a constraint). | | | | | | | | | | | | | | Budget Constraint = | $0.45x1 + $0.90x2 + $0.75x3 <=$1,500 | | | | | | | | | | | | | Space Constraint = | Total Space in Oven = | 192 | Sq Ft | | | | | | | | 27648 | in sq | | | | | She is refilling at half time = | 55296 | in sq | | | | | | | | | | | | | | Space required for a pizza = | 196 | in sq | | | | | for a slice of......

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...Julia 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 athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell. Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time. Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game – 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each......

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...Assignment #3 Case Problem Julia's Food Booth A: Formulation of the LP Model X1(Pizza), X2(hotdogs), X3(barbecue sandwiches) Constraints: Cost: Maximum fund available for the purchase = $1500 Cost per pizza slice = $6 (get 8 slices) =6/8 = $0.75 Cost for a hotdog = $.45 Cost for a barbecue sandwich = $.90 Constraint: 0.75X1 + 0.45X2+ 0.90(X3) ≤ 1500 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 before half time- 27648 x 2 = 55296 Space required for pizza = 14 x 14 = 196 sq. inches Space required for pizza slice = 196/ 8 = 24.50 sq. inches Space required for a hotdog=16 Space required for a barbecue sandwich = 25 Constraint: 24.50 (X1) + 16 (X2) + 25 (X3) ≤ 55296 Constraint: Julia can sell at least as many slices of pizza(X1) as hot dogs(x2) and barbecue sandwiches (X3) combined Constraint: X1 ≥ X2 + X3 = X1 - X2 - X3 ≥ 0 Julia can sell at least twice as many hot dogs as barbecue sandwiches X2/X3 ≥ 2 = X2 ≥2 X3 =X2 - 2 X3 ≥ 0 X1, X2, X3 >= 0 (Non negativity constraint) Objective Function (Maximize Profit): Profit =Sell- Cost Profit function: Z = 0.75 X1 + 1.05 X2 + 1.35 X3 LPP Model: Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3 Subject to 24.5 X1 + 16 X2 + 25 X3 ≤ 55296 0.75 X1 + 0.45 X2 + 0.90 X3 ≤ 1500 X1 - X2 - X3 ≥ 0 X2 - 2 X3 ≥ 0 X1≥ 0, X2≥ 0 and X3 ≥0 Solve the......

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... |Case 3 - Julia's Food Booth | | | | | | | | | | | | | | | | |Constraints: | | | |Available |Usage |Left over | | |Budget ($) |0.75 |0.45 |0.90 | 1,500 | 1,500.00 |0 | | |Oven space (sq. in.) |24 |16 |25 | 55,296 | 50,000.00 |5296 | | |Demand |1 |-1 |-1 |0 | - |0 | | |Demand |0 |1 |-2 |0 | 1,250.00 |-1250 | | | | | | | | | | | |Adjustable Cells | | | | | | | | | |Final |Reduced |Objective |Allowable |Allowable | | |Cell |Name ...

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...Assignment 3 Julia’s food booth A).Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. X1=number of cheese pizza slices X2=number of hot dogs X3=number of BBQ sandwiches Julia Food Booth | | | | | | | | | | | | | | | | Products | Pizza X1 | Hot Dog X2 | Barb Sand X3 | | | | | Profit per unit | $0.75 | $1.05 | $1.35 | Resources | Constraints | | | | Avail | Usage | Left Over | | Budget (i) | $0.75 | $0.45 | $0.90 | 1500 | 1500 | 0 | | Oven Space (ii) | 24 | 16 | 25 | 55,296 | 50000 | 5296 | | Demand (iii) | 1 | -1 | -1 | 0 | -2.3E-13 | 2.27E-13 | | Demand (iv) | 0 | 1 | -2 | 0 | 1250 | -1250 | | | | | | | | | | | | | | | | | | Production | | | | | | | | Pizza | 1250 | | | | | | | Hotdogs | 1250 | | | | | | | Barbecue | 0 | | | | | | | Profit | 2250 | | | | | | | B). If Julia were to borrow money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much additional profit would she make? What factor constrains her from borrowing even more money than this amount? Yes, Julia could increase her profit if she borrowed from a friend. The shadow price is 1.50 for each additional dollar that she earns. This was found by looking at the sensitivity analysis report from the computer solution output. The......

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...Case Problem Julia's Food Booth Assignment #3 Case Problem Julia's Food Booth A: Formulation of the LP Model X1(Pizza), X2(hotdogs), X3(barbecue sandwiches) Constraints: Cost: Maximum fund available for the purchase = $1500 Cost per pizza slice = $6 (get 8 slices) =6/8 = $0.75 Cost for a hotdog = $.45 Cost for a barbecue sandwich = $.90 Constraint: 0.75X1 + 0.45X2+ 0.90(X3) ≤ 1500 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 before half time- 27648 x 2 = 55296 Space required for pizza = 14 x 14 = 196 sq. inches Space required for pizza slice = 196/ 8 = 24.50 sq. inches Space required for a hotdog=16 Space required for a barbecue sandwich = 25 Constraint: 24.50 (X1) + 16 (X2) + 25 (X3) ≤ 55296 Constraint: Julia can sell at least as many slices of pizza(X1) as hot dogs(x2) and barbecue sandwiches (X3) combined Constraint: X1 ≥ X2 + X3 = X1 - X2 - X3 ≥ 0 Julia can sell at least twice as many hot dogs as barbecue sandwiches X2/X3 ≥ 2 = X2 ≥2 X3 =X2 - 2 X3 ≥ 0 X1, X2, X3 >= 0 (Non negativity constraint) Objective Function (Maximize Profit): Profit =Sell- Cost Profit function: Z = 0.75 X1 + 1.05 X2 + 1.35 X3 LPP Model: Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3 Subject to 24.5 X1 + 16 X2 + 25 X3 ≤ 55296 0.75 X1 + 0.45 X2 + 0.90 X3 ≤ 1500 X1 - X2 - X3 ≥ 0 X2 - 2 X3 ≥ 0 X1≥ 0, X2≥ 0 and X3......

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