$1-$ Introduction

The objective of this work is for students to understand how to use decision trees and the expected value framework to make business decisions. The exercise is based on the Alma$-$Caf$$ case study. The case assumes the existence of a Boutique Coffee Shop that is considering various options for expansion and menu changes.

Three different scenarios are provided, each with its own sets of costs, potential gains, and probabilities. The scenarios vary in complexity, from deciding on opening hours, to introducing new menu items, to launching an entirely new coffee blend.

$2-$ Expected results

As part of the business development team, you are expected to elaborate a presentation of maximum of $6$ slides illustrating the provided scenarios and answering the corresponding questions.

$3-$ Provided Scenarios

a$.$ Expanding Working Hours

Alma Cafe is considering expanding their opening hours on Saturdays by $3$ hours. The caf$$ is usually open from $8am$ to $6pm,$ but there's potential for additional revenue if we were to open from $7am$ to $8pm.$ The operations team estimates that that change could generate an extra $$4,000$ in sales each month. However, it would also lead to additional operating costs of $$2,500$ per month. Based on market research and competitor analysis, the management believes there's a $60\%$ chance that the extended hours will attract enough customers to make this worthwhile.

ANSWER:

Should Alma Cafe extend its working hours on Saturdays? Calculate the expected value of this decision and illustrate it on a decision tree.

b$.$ New Product Development

Alma Cafe has the opportunity to introduce a new type of pastry to their menu. Introducing this new pastry requires an initial investment of $$5,000$ in training, marketing, and ingredient procurement. Additionally, maintaining the pastry on the menu will add a fixed operating cost of $$500$ per week.

Based on their customer research, they estimate the following scenarios for the weekly sales over at least a year:

High success: There's a $20\%$ chance that the pastry will be highly popular, selling $350$ units per week at a net profit of $$3$ per unit.

Medium success: There's a $50\%$ chance that the pastry will be moderately popular, selling $200$ units per week at the same net profit per unit.

Low success: There's a $30\%$ chance that the pastry will not be popular, selling only $100$ units per week at the same net profit per unit. In this scenario, the cafe can choose to remove it from the menu after four weeks, limiting their losses.

ANSWER:

Should Alma Cafe introduce the new pastry to their menu? Construct a decision tree to illustrate this problem and calculate the expected value of each decision.

c$.$ New Coffee Blend

Alma Cafe is considering whether to launch a new coffee blend. The cost of the launch, including product development and marketing, is estimated at $$60,000.$ If successful, the new blend is expected to generate a net profit of $$135,000.$ However, there's a chance it could be unsuccessful, in which case it would generate only $$10,000$ in profit. The probability of success is estimated at $55\%.$

Alternatively, the cafe can first conduct a market test costing $$10,000.$ The outcomes of the market test could be positive $(60\%$ probability$)$ or negative $(40\%$ probability$).$ If the market test is positive, the probability of success for the new blend increases to $75\%.$ If the market test is negative, the cafe can choose not to launch the new blend, avoiding further costs.

ANSWER:

Should Alma Cafe launch the new coffee blend immediately, or should they conduct a market test first? Use a decision tree and the expected value framework to answer this question.

Assuming that nothing else is changed, what would be the maximum cost for the Pilot Project we should be willing to pay for the Pilot Project?

Assuming that nothing else is changed, what is the minimum success rate that the Pilot Project should ensure to be willing to pay for it$?$

please can i get a detailed calculation for everything? thank you