Complete the “Julia’s Food Booth” case problem on page 109 of the text. Address each of the issues
Case Study Questions
A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia’s ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
C. If Julia were to borrow some money from a friend before the first game to purchase more ingredients, she feels she can increase her profits. What amount, if any, would you recommend to Julia to borrow?
D. Food prices have been rising lately. Assume purchase costs for the food is now $6.00 for each pizza, $0.75 for each hot dog, and $1.25 for each barbecue sandwich. Repeat the analysis of Part B. What would you recommend to Julia to do at this point?
E. Julia seems to be basing her analysis on the assumptions 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 these uncertainties and the results in (B), (C), and (D), what do you recommend that Julia do? Take into consideration her profit margin for each game.
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