# Mat 540 Assignment 1

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Problem Introduction Julia Robertson, a senior at Tech, is investigating different way to finance her final year at school. She is considering opening a food booth outside the stadium at the home football games. We are asked to formulate and solve the linear program in excel, write the sensitivity ranges for the objective function coefficients and the constraint quantity values then determine if Julia were to borrow some 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 constraints her from borrowing even more money than this amount? There are six (6) home games at the stadium per season. The booth rental per game is \$1000. She will only be able to sell food or drinks, but not both. Julia has decided to sell food. The most popular food items are pizza, hot dogs and BBQ sandwiches. The busiest time will be one hour prior to the game beginning and during half time. Julia was able to secure a deal with a pizza company to deliver 14” pizzas, 8 slices each for \$6 before the game and before half time. Julia found a 3’ x 4’ warming oven she can rent for \$600 or \$100 per game to keep the food warm. She has saved \$1500 to purchase food and supplied for the first game. The money from the games will be used to purchase ingredients for the following games and rental costs. Julia believes this will be a worthwhile venture if she can make \$1000 profit per game after expenses. The information we are given includes the price of items to be sold, fixed costs, variable costs and constraints. Fixed Costs Booth Rental - Per Game Oven Rental - Per Game 1000 100 Prices Pizza per Slice Hot Dogs Each BBQ Sandwich Each 1.5 1.5 2.25 Variable Costs Pizza Per Slice Hot Dogs Each BBQ Sandwiches Each 0.75 0.45 0.9 Profit Pizza One