If a cinnamon roll yields $.25 profit, a donut yields $.20 profit, and a croissant yields $.30 profit, how much profit will be made on each customer? b) if there are 50 customers, how much money can we expect her to make?

Expected Profit per customer = 0.25 * x + 0.2 * y + 0.3 * z

Expected Money to make from 50 Customers = 50 * [ 0.25 * x + 0.2 * y + 0.3 * z]

Explanation:

Assumption:

Let we assume that the customers buying choice is normally distributed with the following probabilities:

Probability of Cinnamon Roll  = x

Probability of Donuts = y

Probability of Croissant = z

Calculation:

As we know that expected profit equals to the sum of the product of probabilities of each item and their corresponding profits. i.e.

Expected Profit per customer = ∑i to n [ Probability of Item i * Corresponding Profit i] whereas n equals total number of items.

therefore we have:

Expected Profit per customer = Probability of Cinnamon Roll * Profit from Cinnamon Roll + Probability of Donuts * Profit from Donuts + Probability of Croissant * Profit from Croissant

By putting values we get:

Expected Profit per customer = x*0.25 + y*0.2 + z*0.3

By rearranging the equation we get:

Expected Profit per customer = 0.25 * x + 0.2 * y + 0.3 * z

For calculating expected money from 50 customers we multiply the expected profit per customer with number of customers as under:

Expected Money to make from 50 Customers = 50 * [ 0.25 * x + 0.2 * y + 0.3 * z]

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