Question

Problem C Suppose you sell cookies on campus. Assume you can buy cookies for $0.50 each and sell them for $2 each. You buy fresh cookies each morning and have to throw away unsold leftovers. If your model for cookie demand is that you will encounter 1000 students in a day and each student has a 2% chance of buying a cookie (independently of one another), how many cookies should you buy in the morning in order to maximize expected profit? What is your expected profit if you buy this many? [Hint: Use the formulas from the example in class, but be careful about what b and l are. Also, definitely use a computer to compute the relevant CDF and expectation. Your answers to both questions should be numbers, not procedures for how a number could be produced.]

Answer 1

In order to maximize expected profit, you should buy 20 cookies in the morning. This way, you can expect to sell all the cookies you buy, resulting in an expected profit of $30.

Step-by-step explanation:

To maximize expected profit, we need to determine how many cookies to buy in the morning. Let's break down the problem:

1. Calculate the probability of selling a cookie to each student:

- Each student has a 2% chance of buying a cookie independently of others.

- This means the probability of selling a cookie to a student is 0.02.

2. Determine the number of potential customers:

- We encounter 1000 students in a day.

3. Calculate the expected number of cookies sold:

- Expected number of cookies sold = Number of potential customers * Probability of selling a cookie to each student

- Expected number of cookies sold = 1000 * 0.02

4. Calculate the expected profit:

- Profit per cookie = Selling price - Cost price

- Profit per cookie = $2 - $0.50 = $1.50

- Expected profit = Expected number of cookies sold * Profit per cookie

Let's plug in the numbers:

• Expected number of cookies sold = 1000 * 0.02 = 20 cookies
• Expected profit = 20 cookies * $1.50 = $30

To maximize expected profit, you should buy 20 cookies in the morning. This way, you can expect to sell all the cookies you buy, resulting in an expected profit of $30.