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Zorluk: Çok zorWeighted Averages in Applied Contexts

A global logistics firm consists of three distinct divisions: Express, Freight, and Solutions. In a given fiscal year, the annual revenue per employee was $120,000\$120,000 for the Express division, $180,000\$180,000 for the Freight division, and $240,000\$240,000 for the Solutions division. The number of employees in the Freight division was 25%25\% greater than the number of employees in the Express division. If the overall weighted average revenue per employee across all three divisions combined was $180,000\$180,000, and the total annual revenue generated by the Solutions division was $14,400,000\$14,400,000, what was the total number of employees across all three divisions?

Cevap: 195 employees

Cevap

The total number of employees across all three divisions was 195.
By setting up the weighted average equation based on employee counts, we establish that the Solutions division headcount equals the Express division headcount (L=E=60L = E = 60). Incorporating the Freight division headcount (F=1.25×60=75F = 1.25 \times 60 = 75) gives a total of 60+75+60=19560 + 75 + 60 = 195 employees.

Adım Adım Çözüm

1
Relate the number of employees in the Freight and Express divisions
F=1.25EF = 1.25E
The Freight division employs 25% more people than the Express division.
2
Set up the weighted average formula and solve for the relationship between Express (EE) and Solutions (LL) headcount
L=EL = E
Setting the overall average revenue per employee to 180,000yields180,000 yields 34.5E + 24L = 40.5E + 18L ,whichsimplifiesto, which simplifies to 6L = 6E$.
3
Calculate the exact employee count of the Solutions division
L=60L = 60
Dividing the total revenue of $14,400,000\$14,400,000 by the revenue per employee of $240,000\$240,000 gives 60 employees.
4
Determine employee counts for all divisions and calculate the total
Total employees = 60+75+60=19560 + 75 + 60 = 195
Since E=L=60E = L = 60 and F=1.25(60)=75F = 1.25(60) = 75, the total employee count is 60+75+60=19560 + 75 + 60 = 195.

Anahtar Kavram

Weighted Average in Combined Sets
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Konular

Weighted Averages in Applied Contexts

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