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Help with a difficult word problem that uses Poisson Distribution


A bakery sells two types of chocolate cakes, A and B. The production cost of cake A
is $20, and of cake B — $30. The bakery sells cake A for $30, and cake B — for $42.
Every day, the bakery makes 20 cakes A and 15 cakes B. If some cakes are left unsold by the end of the
day, they have to throw them away.
There are two types of cake-buying customers. Customers of type I come to the store to buy a cake A,
but if they see that there are no cakes A left, they buy cake B. Customers of type II do the opposite: come
to buy cake B, but if there are none, then they buy cake A. If both A and B are sold out the customers
just leave the store disappointed.
The store owner knows that on average there are 25 customers I per day, and 15 customers II.

• Find a reasonable mathematical model for the bakery. Using the model, compute
• The average revenue per day,
• The average profit (revenue−expenses) per day.
• If you could give an advise to the bakery owner, what you would suggest: increase/decrease production
of cakes A/cakes B? Please, justify (Numerical
experiments (with results of the experiments written down) is a valid justification).
Raising the prices is beyond consideration.

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