Answer :
The correct option for the merger that would give OHaganBooks.com the largest combined customer base is with JungleBooks.com. The combined customer base would be 6,500 customers.
To determine which merger would be most beneficial for OHaganBooks.com, we need to calculate the unique customer base for each competitor and then see which merger results in the largest total customer base.
First, let's calculate the unique customers for OHaganBooks.com, JungleBooks.com, and FarmerBooks.com:
- OHaganBooks.com has a total of 3,500 customers.
- JungleBooks.com has a total of 4,000 customers.
- FarmerBooks.com has a total of 3,800 customers.
Now, let's subtract the shared customers:
- OHaganBooks.com shares 2,000 customers with JungleBooks.com and 1,500 customers with FarmerBooks.com. However, 1,000 customers are shared between all three, so we need to subtract these twice when calculating the unique customers for OHaganBooks.com. Thus, the unique customers for OHaganBooks.com are:
[tex]\[ 3,500 - (2,000 + 1,500 - 1,000) = 3,500 - 2,500 = 1,000 \text{ unique customers} \][/tex]
- JungleBooks.com shares 2,000 customers with OHaganBooks.com and 1,500 customers with FarmerBooks.com. Again, 1,000 customers are shared among all three, so the unique customers for JungleBooks.com are:
[tex]\[ 4,000 - (2,000 + 1,500 - 1,000) = 4,000 - 2,500 = 1,500 \text{ unique customers} \][/tex]
- FarmerBooks.com shares 1,500 customers with OHaganBooks.com and 1,500 customers with JungleBooks.com. Subtracting the 1,000 customers shared among all three, the unique customers for FarmerBooks.com are:
[tex]\[ 3,800 - (1,500 + 1,500 - 1,000) = 3,800 - 2,000 = 1,800 \text{ unique customers} \][/tex]
Now, let's calculate the combined customer base for each merger scenario:
- If OHaganBooks.com merges with JungleBooks.com, the combined customer base would be the sum of OHaganBooks.com's unique customers and JungleBooks.com's total customers, minus the shared customers between the two (since they would now be counted only once):
[tex]\[ 1,000 + 4,000 - 2,000 = 3,000 \text{ customers} \][/tex]
Adding the 3,500 original customers of OHaganBooks.com, the total is:
[tex]\[ 3,000 + 3,500 = 6,500 \text{ customers} \][/tex]
- If OHaganBooks.com merges with FarmerBooks.com, the combined customer base would be the sum of OHaganBooks.com's unique customers and FarmerBooks.com's total customers, minus the shared customers between the two:
[tex]\[ 1,000 + 3,800 - 1,500 = 3,300 \text{ customers} \][/tex]
Adding the 3,500 original customers of OHaganBooks.com, the total is:
[tex]\[ 3,300 + 3,500 = 6,800 \text{ customers} \][/tex]
Comparing the two scenarios, merging with JungleBooks.com would result in a larger combined customer base of 6,500 customers, compared to 6,800 customers if merging with FarmerBooks.com. Therefore, the best option for OHaganBooks.com is to merge with JungleBooks.com to achieve the largest combined customer base."
OHaganBooks.com should merge with JungleBooks.com as it would result in a larger combined customer base of 4,500 customers. Merging with FarmerBooks.com would result in a combined customer base of 4,300 customers. Therefore, JungleBooks.com is the better option.
Let's break down the information given and calculate the combined customer base for both potential mergers.
OHaganBooks.com and JungleBooks.com share 2,000 customers, but 1,000 of these are also shared with FarmerBooks.com.
OHaganBooks.com and FarmerBooks.com share 1,500 customers, but 1,000 of these are also shared with JungleBooks.com.
JungleBooks.com and FarmerBooks.com share 1,500 customers.
OHaganBooks.com: 3,500 - 2,000 (shared with JungleBooks.com) - 1,500 (shared with FarmerBooks.com) + 1,000 (shared with both) = 1,000 unique customers.
JungleBooks.com: 4,000 - 2,000 (shared with OHaganBooks.com) - 1,500 (shared with FarmerBooks.com) + 1,000 (shared with both) = 1,500 unique customers.
FarmerBooks.com: 3,800 - 1,500 (shared with OHaganBooks.com) - 1,500 (shared with JungleBooks.com) + 1,000 (shared with both) = 1,800 unique customers.
Merging with JungleBooks.com:
Unique customers: OHaganBooks.com (1,000) + JungleBooks.com (1,500) = 2,500
Shared customers: 2,000
Total: 2,500 + 2,000= 4,500
Merging with FarmerBooks.com:
Unique customers: OHaganBooks.com (1,000) + FarmerBooks.com (1,800) = 2,800
Shared customers: 1,500
Total: 2,800 + 1,500 = 4,300
Therefore, merging with JungleBooks.com would give OHaganBooks.com a larger combined customer base of 4,500 customers.
