Julia's Food Booth

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Julia’s Food Booth Case Problem A. X1 = pizza slices, X2 = hot dogs, and X3 = barbeque sandwiches. Maximize Z = ($0.75 X1) + ($1.05 X2) + ($1.35 X3) Subject to: ($0.75 X1) + ($0.45 X2) + ($.90 X3) less than or equal to $1,500 (24 X1) + (16 X2) + (25 X3) less than or equal to 55,296 inches squared oven space X1 greater than or equal to X2 + X3 (X2/X3) greater than or equal to 2.0 X1, X2, X3 greater than or equal to 0 Solution: X1 = 1250 pizza slices X2 = 1250 hot dogs X3 = 0 barbeque sandwiches Z = $2,250 Based upon this information, Julia will generate revenues of $2,250 for her first game. Her leasing of the booth will cost her $1,000/game, so she is left with $1,250. Additionally, the cost of leasing the warming oven is 600 for 6 games, and that equates to $100/game. This gives her profit of $1,150 for her first game. One aspect of this model that is more complex relates to the $1,500 used to buy the food items. Since the objective function reflects net profit, the $1,500 is recouped and can be used for the next home game to purchase food ingredients. This allows Julia not to have to use of her $1,150 profit to buy ingredients for the next game. B. Yes, she would be able to increase her profit if she were to borrow some money from a friend before the first game to purchase more ingredients. The dual value is $1.50 for each additional dollar. The upper limit of the sensitivity range for budget is $1,658.88, so she should only borrow approximately $158. Her additional profit would be $238.32 or a total profit of $2,488.32. C. Yes, Julia should definitely hire her friend to assist with selling at each game. It would be virtually impossible for Julia to prepare all of the food items generated in the solution in the limited time period she had since she cannot cook while she si selling. The additional profit Julia would generate if she

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