Case Problem Page 109: The Possibility At Restaurant Angela

Question

Case Problem Page 109the Possibility Restaurantangela Fox And Z Angela Fox and Zooey Caulfield, food and nutrition majors at State University and close friends, decided to open a French restaurant named “The Possibility” in Draperton, a small town with no existing French restaurants. Their initial plan was to serve only two full-course meals each night—one with beef and one with fish—due to uncertainty about local tastes and limited resources. They aimed to evaluate customer preferences through experimentation with different appetizers, soups, salads, vegetables, and desserts. The challenge was to determine how many meals to prepare each night within their resource constraints. They estimated a maximum of 60 meals sold per night. Each fish dinner, including accompaniments, takes 15 minutes to prepare; a beef dinner requires twice as long, at 30 minutes. There are 20 hours of kitchen staff available daily. They anticipated a demand ratio of at least three fish dinners for every two beef dinners, and also expected that at least 10% of customers would order beef dinners. Profit estimates are $12 per fish dinner and $16 per beef dinner. They also considered scenarios such as increasing the fish dinner price to equalize profits, adjusting demand assumptions, and evaluating the impact of advertising, staffing reliability, and price changes on their profit and operational planning.

Dr. Jack HW Helper · Accepted Answer

Angela Fox and Zooey Caulfield's venture into the restaurant industry exemplifies strategic planning under resource constraints. They sought to optimize their nightly meal preparation to maximize profit while accommodating demand uncertainties, staffing limitations, and market perceptions. Using linear programming as a decision-support tool, they formulated models to determine the optimal number of fish and beef dinners to prepare nightly, considering constraints such as preparation time, maximum sales volume, and customer demand ratios. The fundamental goal was to maximize profit subject to operational constraints. Let $ x $ denote the number of fish dinners and $ y $ denote the number of beef dinners prepared each night. The profit function was expressed as: $$ \text{Maximize } Z = 12x + 16y $$ Subject to constraints: Preparation time: $ 15x + 30y \leq 1200 $ minutes (since 20 hours = 1200 minutes) Sales volume: $ x + y \leq 60 $ Demand ratio: $ x \geq 1.5 y $ (three fish for every two beef) Minimum beef orders: $ y \geq 0.1 (x + y) $ or alternatively, $ y \geq 0.1(x + y) $, which simplifies to $ 0.9 y \geq 0.1 x $ By solving this LP model using Excel Solver or similar software, Angela and Zooey could identify the optimal mix of meals that maximizes profitability while respecting operational constraints. For example, increasing the fish dinner profit to $14 to match the beef dinner profit alters the profit function but may or may not influence the optimal solution depending on the demand sensitivity and constraints. Adjusting demand assumptions, such as increasing the proportion of customers ordering beef to 20%, directly impacts the optimal meal plan. A higher demand for beef increases the incentive to prepare more beef dinners, potentially shifting the optimal point. Similarly, an advertising campaign boosting maximum sales from 60 to 70 meals per night could enhance profit margins, but the cost-effectiveness of such advertising needs evaluation.

Case Problem Page 109: The Possibility At Restaurant Angela

Case Problem Page 109the Possibility Restaurantangela Fox And Z

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Case Problem Page 109the Possibility Restaurantangela Fox And Z

Sample Paper For Above instruction

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