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 is uncertain, but historically it follows a normal distribution, with an average demand of 1,100 tarts, with a standard deviation of 250.

The tarts at the farmer's market sell for $4.00 each. If there are tarts left over after the farmer's market closes, the baker has a deal with a local coffee shop that 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 it will accept a maximum of 100 leftover tarts, a 20% chance that it will accept a maximum of 125 tarts, and a 10% chance they will accept a maximum of 150 tarts. If there are more tarts left over 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. Calculate the average and standard deviation of profit for each batch quantity. Also, determine the standard error and the 95% confidence interval for each.

1. Which of the following is an uncertainty (random variable) in this model?

a. Coffee Shop Demand

b. Production Cost per dozen

c. Baking Quantity (in Batches)

d. Per Unit Cost of Lost Profit

2. Which of the following is the decision variable in this model?

a. Coffee Shop Demand

b. Farmer's Market Demand

c. Baking Quantity (in Batches)

d. There is no decision variable in this model

3. When does the Cost of Lost profits occur?

a. When the number of tarts produced exceeds the farmer's market demand.

b. When the number of tarts produced is less than the farmer's market demand.

c. When the number of tarts produced exceeds the coffee shop demand.

d. When the number of tarts produced is less than the coffee shop demand.

4. This question will require you to alter your model to test your calculations.

Set the Batches Produced to 70, set Farmers Market Demand at 1200, and set the Coffee Shop Demand to 100.

What is the cost of lost profits with these settings?

5. Set the Batches Produced to 70, set Farmers Market Demand at 1200, and set the Coffee Shop Demand to 100.

What is theTotal Profit with these settings?

6. This question will require you to alter your model to test your calculations.

Set the Batches Produced to 110, set Farmers Market Demand at 1200, and set the Coffee Shop Demand to 100.

What is the Total Profit with these settings?