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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