You are in the process of planning the opening of a restaurant, a venture that demands careful consideration, particularly in terms of the various associated costs. While you have some insights into specific expenses, the unpredictable nature of demand remains a significant factor. Your initial assessment reveals a fixed cost of $$700,$ with an additional $$650$ for overhead. Food preparation costs vary depending on the menu, typically ranging from $$5-$ $$10$ per meal $($uniformly distributed$).$ Demand tends to fluctuate, with weekends experiencing higher activity compared to weekdays, and afternoons being more popular than mornings. However, taking into account the restaurant's proximity to a bustling area, you estimate that weekly demand is normally distributed, with an average weekly demand of $285$ meals, and a standard deviation of $20.$

At this point, you find yourself contemplating the pricing strategy for your meals, with two options on the table. The first option involves setting an average meal price of $$14,$ while the second proposes pricing each meal at $$16,$ albeit with a potential trade$-$off of a reduction in customer footfall, resulting in an average of $250$ customers per week, standard deviation remains the same. Consider all costs on a weekly basis.

The objective of this simulation is to determine the optimal price to set, specifically, whether it should be set at $$14$ or $$16,$ what will be the profit and risk of loss in each case, and the associated risk of loss. Conduct $500$ simulations for both scenarios, aiming to build a case for your preferred option.

Format of assignment: Provide a table showing the following information

Cover page showing the title of assignment and your name$/$student id

Summary table $(8=$ points$)$

Stats when price is set to $$14$

Descriptive Stats

Values

Average profit $(1$ point$)$

Maximum profit $(1$ point$)$

Minimum profit $(1$ point$)$

Risk of loss $(1$ point$)$

Stats when price is set to $$16$

Average profit $(1$ point$)$

Maximum profit $(1$ point$)$

Minimum profit $(1$ point$)$

Risk of loss $(1$ point$)$

Scatter plots: for both scenario $(6$ points $=3*2$ plots$)$

Snapshots of process from excel for both scenarios. Do not copy paste, take snapshots $(4$ points $=2*2$ snapshots$)$

Conclusion: Which pricing strategy you would choose? Articulate your findings from the scatterplot, including insights on average profit, maximum and minimum profit values, and the associated risk of loss $(2$ points$)$