A local baker sells fresh fruit pastries at the farmer's market every Saturday. The baker wants to establish a consistent baking policy to simplify planning for each weekend. Demand for the pastries is uncertain, but average sales have been about 200 pastries, with a standard deviation of 25 pastries.
At the farmer's market, the pastries sell for $4.00 each. If there are pastries leftover after the market closes, a local coffee shop may buy some of the leftover pastries for $1.60 each for resale in their shop. How many pastries the coffee shop will take is uncertain, and depends on their anticipated demands. There is a 30% chance the coffee shop will accept a maximum of 50 leftover pastries, a 40% chance that they will accept a maximum of 20 leftover pastries, a 20% chance that they will accept a maximum of 10 pastries, and a 10% chance they will not accept any pastries. If there are more pastries leftover than what the coffee shop will accept, they will be donated to a local food pantry and there will be no additional revenues from those pastries.
The production cost of a batch of pastries is $20.00. There are a dozen pastries per batch.
The farmer's market is full of competition and the baker will lose customers if he is unable to meet demand. He views this as a cost of lost profit, and will assume a loss of $1.00 per unit of unmet demand.
Compare baking policies from 15 batches to 24 batches. Run 1000 iterations of the model.
Analyze your results to determine the best baking quantity to maximize profit.
Questions:
1- Please provide the Simulation Modeling with all necessary inputs and decisions (Decision, Uncertainty and Output). Show the formulas and calculations used.
2- Make the following changes and show formula with calculations:
Set the Number of Batches produced to 15
Set the Farmer's Market Demand to 200
Set the Coffee Shop Demand to 10
What is the cost of lost profits under these conditions?
What is the total profit with these settings?
What is the total production cost with these settings?
What is the total revenue with these settings?
3 - Make the following changes and show formula with calculations:
Set the Number of Batches produced to 18
Set the Farmer's Market Demand to 200
Set the Coffee Shop Demand to 10
What is the revenue from the coffee shop with these settings?
4- After analyzing the results of your simulation, which baking policy would you recommend and why?