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The problem presented is a classic example of a **newsvendor (or newsboy) problem** in inventory management, where the goal is to determine the optimal order quantity that maximizes expected profit.

### Given Data:
1. **Demand Levels and Probabilities**:
   - Crates demanded: 700, 1050, 1400, 1750
   - Corresponding frequency (days out of 100): 20, 25, 40, 15
   - Probabilities:
     \[
     P(700) = \frac{20}{100}, \ P(1050) = \frac{25}{100}, \ P(1400) = \frac{40}{100}, \ P(1750) = \frac{15}{100}
     \]

2. **Costs and Selling Prices**:
   - **Cost price per crate** = ₹250
   - **Selling price per crate (if sold same day)** = ₹400
   - **Salvage value (if not sold the same day)** = ₹150

### Step 1: Calculate the Expected Profit for Each Possible Order Quantity
We will compute the expected profit for each of the demand levels (700, 1050, 1400, and 1750) to find the optimal number of crates the dealer should order.

- **Case 1**: If the order quantity is less than or equal to the demand, all crates are sold at ₹400.
- **Case 2**: If the order quantity exceeds the demand, the unsold crates are salvaged at ₹150.

We can now compute the expected profit for each possible order quantity (700, 1050, 1400, and 1750).

### Step 2: Find the **Expected Value of Perfect Information (EVPI)**

EVPI measures the value of knowing the exact demand in advance. It can be calculated as:
\[
EVPI = E[\text{Profit with perfect information}] - E[\text{Profit with optimal order quantity}]
\]

Let me now compute the expected profits and the EVPI. I will begin by calculating the probabilities, expected profits for each order quantity, and then the EVPI.It looks like I encountered an issue with processing the expected profits and EVPI. However, I can explain the process in detail for you to follow through manually if you'd like. Here's the approach to solving the problem:

### Step-by-Step Process:

1. **Calculate Expected Profit for Each Order Quantity:**
   For each order quantity (700, 1050, 1400, and 1750 crates), the expected profit is determined based on the probabilities of each demand scenario. The formula for each demand scenario is:
   \[
   \text{Profit} =
   \begin{cases}
   \

The number of crates of mangoes demanded and frequency of each level of demand in a period of 100 days are given below:

No. of Crates Demanded: 700, 1050, 1400, 1750
No. of Days: 20, 25, 40, 15

It costs ₹250 to buy a crate. The selling price of each crate, if sold the same day, is ₹400; but if it is not, the crate with stale fruits has a salvage value of ₹150. How many crates should a dealer order every day so that his profits may be maximized? Also find the EVPI.

Explore the newsvendor problem for maximizing profits with varying demand levels for mango crates. Learn how to calculate the expected profits and determine the optimal order quantity to avoid losses, considering costs, selling prices, and salvage values. Includes a detailed approach to calculating EVPI.

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