Question
A sales manager wishes to assign four sales territories to four salespersons. The salespersons differ in their ability and skills and consequently the sales expected in each territory are different. The estimates of sales per month for each sales-person in different territories are given below:
Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.
Answer :
Word Count : 857
To solve this problem, we need to find the optimal assignment of four salespersons to four different territories such that the total monthly sales are maximized. This is a classic example of the Assignment Problem, which can be efficiently solved using the Hungarian Algorithm. ### Step 1: Understand the Problem We have a 4x4 matrix where each cell represents the sales a salesperson can achieve in a specific territory. Our goal is to assign each salesperson to a unique territory to maximize the total sales. ### Step 2: Prepare the Data First, we need to extract the sales data from the provided image. Since the image is not directly accessible, I'll assume a sample matrix for demonstration purposes. Let's assume the sales matrix is as follows: | Salesperson \ Territory | Territory 1 | Territory 2 | Territory 3 | Territory 4 | |-------------------------|-------------|-------------|-------------|-------------| | Salesperson A | 10 | 19 | 8 | 15 | | Salesperson B | 17 | 21 | 16 | 18 | | Salesperson C | 12 | 14 | 10 | 13 | | Salesperson D | 20 | 16 | 14 | 19 | ### Step 3: Apply the Hungarian Algorithm The Hungarian Algorithm involves the following steps: 1. Subtract the smallest element in each row __________ _________ _____ _________ ______ _________ ___ ______ ____ ______.
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To solve this problem, we need to find the optimal assignment of four salespersons to four different territories such that the total monthly sales are maximized. This is a classic example of the Assignment Problem, which can be efficiently solved using the Hungarian Algorithm. ### Step 1: Understand the Problem We have a 4x4 matrix where each cell represents the sales a salesperson can achieve in a specific territory. Our goal is to assign each salesperson to a unique territory to maximize the total sales. ### Step 2: Prepare the Data First, we need to extract the sales data from the provided image. Since the image is not directly accessible, I'll assume a sample matrix for demonstration purposes. Let's assume the sales matrix is as follows: | Salesperson \ Territory | Territory 1 | Territory 2 | Territory 3 | Territory 4 | |-------------------------|-------------|-------------|-------------|-------------| | Salesperson A | 10 | 19 | 8 | 15 | | Salesperson B | 17 | 21 | 16 | 18 | | Salesperson C | 12 | 14 | 10 | 13 | | Salesperson D | 20 | 16 | 14 | 19 | ### Step 3: Apply the Hungarian Algorithm The Hungarian Algorithm involves the following steps: 1. Subtract the smallest element in each row __________ _________ _____ _________ ______ _________ ___ ______ ____ ______.
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