Question

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. Based on the results of your analysis, indicate your recommended decision in the textbox on the right.

Answer 1

A ) option iv) is right.When the number of tarts produced is less than the farmer's market demand.

since they have given in the data about lost profit as 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.

first, calculate the lost revenues and second, calculate the cost associated with generating the lost revenues. The difference between the two generally constitutes the lost profits.

B) baking quantity

c) no of batches = 60; no of tarts per batch = 12; total no of tarts = 12x60 = 720;

production cost ber batch = $ 20 ; total cost of producing 60 batches = 60 X 20 = 1200;

selling price of each tart = $ 3 and total price = 720 X 3 = 2160;

cost of lost profit for each taught = $1; total lost profit = 1200 - 720 = 480 X 1 = $ 480 ;

c) total production cost = $1200; total cost = 1200 + 480 = 1680;( considering lost profit )

d) total profit = 2160 - 1680 = $480

e) if we go for a batches of 110 it gives you more profit ;

110 batches produces nearly 110 X 12 = 1320;

1200 farmers market demand and remaining 120 where coffee shop can take 100 with 40 % chance and remaining 20 is donated to local food pantry;

total revenue he obtain = 3600 + 1500 = 5100;

total cost = 110 X 20 = 2200;

maximum profit is 2900;

where no lost profit takes place

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