Question

A fruit importer sells Brazilian mango to the New England area. Mangos need to be purchased from growers in Brazil at a cost of $50 per box. The importer sells fresh mangos to local groceries at a price of $90 per box. Unsold mangoes after the season will be sold at a discounted price of $20 per box. It is estimated that the importer’s demand follows a discrete probability distribution as given below:

Demand (in boxes) 100 200 300 400 500 600
Probabiltiy 0.1 0.2 0.3 0.2 0.1 0.1
Determine how many boxes of mangoes should the importer purchase?

Answer 1

To determine how many boxes of mangoes the importer should purchase, calculate the expected demand and compare it with the importer's supply.

Step-by-step explanation:

To determine how many boxes of mangoes the importer should purchase, we need to calculate the expected demand and compare it with the importer's supply. The expected demand can be calculated by multiplying the demand for each quantity level by its probability and summing up the results. In this case, the expected demand is calculated as follows:
Expected demand = (100 * 0.1) + (200 * 0.2) + (300 * 0.3) + (400 * 0.2) + (500 * 0.1) + (600 * 0.1) = 290
Since the importer sells fresh mangos at $90 per box, and the cost of purchasing a box from growers in Brazil is $50, the importer will make a profit of $40 per box. Therefore, the importer should purchase enough boxes to meet the expected demand of 290 boxes.