Julia’s Food Booth – the Problem and the Model
Quantitative Methods -MAT 540
Julia’s Food Booth
Assignment #3
The Problem and the Model
Julia is analyzing whether to open a food booth during her school’s home games in order to earn some money for her tuition. The booth costs $1,000 per game. She is constrained by the available space in a warming oven, as well as her available cash of $1,500 to purchase the supplies for the first game. If her business plan indicates that she will clear a profit of at least $1,000 per game, she will move forward with her plan.
The model for this problem is set up in Excel. Data for profit, cost, and needed warming oven space for each food item are input into labeled cells. Relevant parameters are then loaded into Solver, including two additional constraints related to expected sales of pizza and hot dogs. The income statement created based on Solver’s solution indicates that Julia will make a profit of just over $1,000 after she pays for the booth rental ($1000) and the $100 for the warming oven ($600 for 6 home games), so the food booth seems to be a good prospect for her.
Borrowing Money
Because the original model shows that the optimal combination of food items for the beginning cash available of $1,500 leaves space available in the warming over, Julia may have some leeway to purchase more food items in an effort to increase her profits. If she borrows $250 from someone, she can purchase enough additional ingredients to fill all of the space in her warming over. Her net profit increases by about $300. When she repays the money she borrowed, she will have an extra $90 in hand. It does no good for her to borrow more than this, since there would not be enough space in the oven to keep the food warm during the games.
Hiring a worker
Under the original model, Julia’s profit is too near her goal of $1,000 to cover the additional expense of hiring help. However, if Julia borrows money at the beginning, she increases her potential profit by about $300 per game. Under this scenario, she can afford to hire her friend and still increase her profit by approx. $200. This would probably be a good idea