You are the proud owner of a local coffee shop. Business is good, but you're looking to optimize your operations.

Using the concepts covered this week, discuss the following:

1. Marginal Analysis for Optimal Activity: You're considering adding new pastries to your menu. How can you use marginal cost (MC) and marginal revenue (MR) to decide if this is a good idea? At what point should you stop adding pastries to maximize your profit?
2. Irrelevant Costs: You're reviewing your financial statements and see fixed costs like rent and equipment depreciation. Why are these costs irrelevant when deciding whether to add new pastries?
3. Employee Scheduling: You need to decide how many baristas to schedule for the weekend rush. How can you use marginal analysis to find the optimal staffing level? What factors, besides labor costs, might influence your decision?
4. Constrained Optimization: Imagine you have limited display space for pastries. Can you use marginal analysis to find the optimal mix of different pastry types to maximize your profit while respecting this constraint?

Explanation:

This question focuses on applying marginal analysis to real-world business decisions:

• Marginal Analysis: This helps determine the optimal level of activity by comparing marginal revenue (the additional revenue from each additional unit) with marginal cost (the additional cost of producing each additional unit). You should add pastries until the point where MR = MC.
• Irrelevant Costs: Fixed costs are incurred regardless of your production level. They don't change with your decision about adding pastries, so they shouldn't be considered.
• Employee Scheduling: You should hire additional baristas until the marginal benefit of the additional sales they generate (marginal revenue) equals the marginal cost of hiring them (wages).
• Constrained Optimization: Even with limited space, you can find the optimal mix of pastries by comparing the marginal revenue per unit of display space for each pastry type. Choose the pastries that offer the highest marginal revenue per unit space until the constraint is met.