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An office manager is charged with staffing. His first hire costs $15/
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06 Mar 2024, 01:33
06 Mar 2024, 01:33
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Question Stats:
8% (01:37) correct
91% (01:46) wrong based on 12 sessions
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An office manager is charged with staffing. His first hire costs $15/hr, and generates revenue of $20/hr.This employee can work at 100% efficiency. Each additional employee hired can only work at 90% of the efficiency of the previous hire. What is the maximum number of employees he can hire before the employee costs more than the revenue he generates?
A. 2
B. 3
C. 4
D. 5
E. cannot be determined
A. 2
B. 3
C. 4
D. 5
E. cannot be determined
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Joined: 11 Nov 2023
Posts: 207
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WE:Business Development (Advertising and PR)
Re: An office manager is charged with staffing. His first hire costs $15/
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07 Mar 2024, 20:59
07 Mar 2024, 20:59
1
Let n = the nth employee hired after the first
The profit generated by the nth employee = (20 * 0.9^n) - 15
The employee costs more than revenue generated when (20 * 0.9^n) - 15 ≤ 0
When n = 1, (20 * 0.9^1) - 15 = 18 - 15 = 3
When n = 2, (20 * 0.9^2) - 15 = 16.2 - 15 = 1.2
When n = 3, (20 * 0.9^3) - 15 = 14.58 - 15 = -0.42
Thus, the max he can hire is 2 additional + 1st employee = 3.
The profit generated by the nth employee = (20 * 0.9^n) - 15
The employee costs more than revenue generated when (20 * 0.9^n) - 15 ≤ 0
When n = 1, (20 * 0.9^1) - 15 = 18 - 15 = 3
When n = 2, (20 * 0.9^2) - 15 = 16.2 - 15 = 1.2
When n = 3, (20 * 0.9^3) - 15 = 14.58 - 15 = -0.42
Thus, the max he can hire is 2 additional + 1st employee = 3.
gmatclubot
Re: An office manager is charged with staffing. His first hire costs $15/ [#permalink]
07 Mar 2024, 20:59
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