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26 February, 19:22

Gotham City has 10,000 streetlights. City investigators have determined that at any given time, an average of 1,000 lights are burned out. A street light burns out after an average of 100 days of use. The city has hired Mafia, Inc., to replace burned-out lamps. Mafia, Inc.'s contract states that the company is supposed to replace a burned-out street lamp in an average of 7 days. Do you think that Mafia, Inc. is living up to the contract

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  1. 26 February, 20:05
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    11.11

    Explanation:

    λ=1/100/day

    K=10,000

    Therefore the expected length of time for replacing a burned-out lamp is equally the expected waiting time in the system which is W.

    L = 1,000 (average number of burned-out lamps)

    Effective arrival rate:

    ¯λ=λ (K-L) = 1/100 (10,000-1,000) = 90/day

    Average length of time it takes to replace a burned-out lamp is:

    W=L/¯λ = 1,000/90 = 11.11

    Mafia, Inc. is not living up to the contract since the company is supposed to replace the burned-out street lamp in an average of 7 days.
  2. 26 February, 20:12
    0
    This means that Mafia, Inc. is NOT living up to the contract (

    Explanation:

    We can relate this question to machine repair problem M/M/1.

    Using the formula λ*=λ (K-L)

    Where λ is average days of usage = 1/100 per day

    K is Total sample of streetlights = 10000

    L is the average number of burned-out lamps = 1000

    The expected length of time for replacing a burned-out lamp is the expected waiting time given by W = L/λ*

    Therefore the effective arrival rate λ*=λ (K-L) = 1/100 (10000-1000)

    = 90/day

    Thus, the average length of time it takes to replace a burned-out lamp is

    W=L/λ * = 1000/90≈11.11 days

    This means that Mafia, Inc. is NOT living up to the contract (contract states that the company is supposed to replace a burned-out street lamp in an average of 7 days).
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Home » Business » Gotham City has 10,000 streetlights. City investigators have determined that at any given time, an average of 1,000 lights are burned out. A street light burns out after an average of 100 days of use. The city has hired Mafia, Inc.
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