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 - Which of the following is an uncertainty (random variable) in this model?
Baking Quantity (in Batches)
Production Cost
Cost of Lost Profit
Coffee Shop Demand
2 - Which of the following is the decision variable in this model?
When the number of pastries produced exceeds the coffee shop demand.
When the number of pastries produced exceeds the farmers market demand.
When the number of pastries produced is less than the coffee shop demand.
When the number of pastries produced is less than the farmer's market demand.
3 - Please show the formulas and calculations used.