Question

The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2.50 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $3 each, find the probability distribution for her daily profit.

Answer 1

Probability No. of pies Cost Revenue Profit

0.5 100 500 300 -200

0.25 150 500 450 -50

0.25 200 500 600 100

Explanation:

We are given that The owner believes that on 50% of the days she sells 100 pies.

So, Probability of selling 100 pies = 0.5

On another 25% of the days she sells 150 pies

So, Probability of selling 150 pies = 0.25

She sells 200 pies on the remaining 25% of the days

So, Probability of selling 200 pies = 0.25

We are given that the owner bakes 200 pies each day at a cost of $2.50 each.

So, Cost per day =
`200 * 2.50 =500`

Probability No. of pies Cost

0.5 100 500

0.25 150 500

0.25 200 500

Now we are given that she sells the pies for $3 each

So, SP of 100 pies =
`3 * 100 = 300`

SP of 150 pies =
`150 * 3 = 450`

SP of 200 pies =
`200 * 3 = 600`

Probability No. of pies Cost Revenue Profit

0.5 100 500 300 -200

0.25 150 500 450 -50

0.25 200 500 600 100