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Assignment 3: Julia’s Food Booth
Professor Hines
Quantitative Methods
December 9, 2012

Julia Robertson who is a senior at Tech, she has been investigating different ways to finance her final year at school. She is considering leasing a booth at home games where she will be selling hotdogs, pizzas, BBQ sandwiches. In this report I will formulate and solve and L.P model, Evaluate the prospect of borrowing money before the first game, Evaluate the prospect of paying a friend $100/ game to assist, and finally analyze the impact of uncertainties on the model.

In the Linear program, x1 will represent pizza, x2 will represent hotdogs, and x3 will represent BBQ. My first constraint in the Linear program was Budget. The maximum fund available for Julia purchase is $1500. The cost for pizza is that each pizza will cost her $6 and will include 8 slices so the calculation I did was 6/8=0.75 for the cost per pizza. The cost for a hotdog was .45 and for the cost for a BBQ sandwich was .90 which both were giving in the book. The constraint was 0.75x1+0.45x2+0.90x3< than equal to 1500. The second constraint was the Oven Space. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. Julia has plans to fill the oven with the three food items before the game and then again before half time. The 3 feet by 4 feet I converted to square inches 3ft converted to square inches give me 36 and 4ft converted to square inches give me 48 and I just multiply them and it give me 1728 sq. inches. Then I will multiply the 1728 by the number of shelves she has which is 16 and the total for that is 27648 sq. inches. The oven will be refilled before half time 27648 * 2 which gives me 55296. The space required for the pizza is 14 *14 and I converted that into sq. inches which give me 196 sq. inches. The space required for pizza slice = 196/8=24.50 or 25. The space required for hotdog and bbq sandwich which were giving in the book were 16 and 25. The constraint was 25x1+16x2+25x3x2+x3 I have to get everything on one side and equal to zero. The constraint will be x1-x2-x3> than equal to 0. Final constraint is that Julia can sell as least twice as many hot dogs as BBQ sandwiches. X2/x3> than equal to 2=x2>2x3=0. If Julia were to borrow some more 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 factors constrains her from borrowing even more money than this amount (indicated in your answer to the previous question)? Julia will not have to borrow any money from a friend Julia plans to sell a slice of pizza and hotdog for $1.50 apiece and a BBQ sandwich for $2.25. Pizza Hot dog BBQ $1.50-.75=.75 $1.50-.45=1.05 $2.25-.90=1.35 Maximum Profit=.75x1+1.05x2+1.35x3=.75(1250) +1.05(1250) +1.35(0) =2250-1000=1250-100=$1150 According to my calculation Julia will not need to borrow money from her friend, once she pay the amount of 1000 for the food booth and 100 for the lease warmer oven she has left over the amount of $1150. Hopefully Julia will continue to make the profit because she will still have to pay 100 for the each six games for leasing the oven warmer. When Julia looked at the solution in (A), she realized that it would physically difficult for her to prepare all the hot dogs and BBQ sandwiches indicated in this solution. She believes she can hire a friend of hers to help her for $100 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should do? In the above graph the upper bound informs us of the most profit Julia can make. Her upper bound limit is 1618.42. Her original budget is 1500.00. Julia would have 118.42 (1618.42 – 1500.00) to pay her friend per game. The 118.42 also indicates what Julia can borrow without losing profit but she makes enough that she shouldn’t have to borrow anything. For every dollar Julia makes she can invest 1.50 into the business. Julia seems be basing her analysis on the assumption that everything will go as she plans. What are some of the uncertain factors in the model that could go wrong and adversely affect Julia’s analysis? Given uncertainties and the results in (A), (B), and (C), what do you recommend that Julia do? The game could get cancel due to the weather, there is nothing Julia can really do if the game get cancel due to the weather they only thing I can think of is if they make up that game just make sure she attends it. Julia friend who is helping her may get sick, Julia should have another person such as a friend or a family who will be willing to help out just in case. Competition between other booth at the games, Julia could either work with others at the booth or she could start offering out special or even do ho BBQ sandwiches, hotdogs, pizzas combos just to outstand her competition.

Reference: 1. Taylor, B. M. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

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