A local baker sells fresh fruit tarts at the farmer's market every Saturday. He wants to establish a consistent baking policy to simplify planning for each weekend. Demand for the tarts at the farmer's market is uncertain, but historically it follows a normal distribution, with an average demand for 1,200 tarts , with a standard deviation of 400.
The tarts at the farmer's market sell for $3.00 each. If there are tarts leftover after the farmer's market closes, the baker has a deal with a local coffee shop who agrees to buy some of the leftover tarts for $1.50 each for resale in their shop.
How many tarts the coffee shop will take is also uncertain, and depends on their anticipated demands. There is a 30% chance the coffee shop will accept a maximum of 50 leftover tarts, a 40% chance that they will accept a maximum of 100 leftover tarts, a 20% chance that they will accept a maximum of 125 tarts, and a 10% chance they will accept a maximum of 150 tarts. If there are more tarts 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 tarts.
The production cost of a batch of tarts is $20.00. There are a dozen tarts 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. (There is no associated cost of lost profit for coffee shop sales.)
Compare baking policies of 70 batches up to 140 batches in increments of 10. Run 1000 iterations of the model.
Analyze your results with statistical analysis. At the very least, make sure you calculate the average and standard deviation of profit for each batch quantity.