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notka56 [123]
2 years ago
11

Consider a two-server parallel queuing system where customers arrive according to a poisson process with rate λ, and where the s

ervice times are exponential with rate μ. moreover, suppose that arrivals finding both servers busy immediately depart without receiving any service (such a customer is said to be lost), whereas those finding at least one free server immediately enter service and then depart when their service is completed. (a) if both servers are presently busy, find the expected time until the next customer enters the system. (b) starting empty, find the expected time until both servers are busy. (c) find the expected time between two successive lost customers.
Business
1 answer:
lara31 [8.8K]2 years ago
7 0
<span>I would assume that customers arrive at the queue according to the poisson process, and then decide whether to enter the queue or leave as per the rules in the question. for (a) I interpret "enter the system" as "join the queue". The expected time for this will be E(time until there is a free slot) + E(time for someone to arrive once a slot is free). Noting that the additional time taken for someone to arrive once a spot is free is independant of the time that the slot became free (memorylessness property of poisson process) The waiting time of a Poisson(\lambda) is exp(\lambda) with mean \frac{1}{\lambda} E(\text{Time someone enters the system})=\frac{1}{2\mu} + \frac{1}{\lambda} Your post suggests you already understand where \frac{1}{2\mu} comes from.</span>
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Masterson, Inc., has 4.1 million shares of common stock outstanding. The current share price is $84, and the book value per shar
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Answer:

The answer is "8.37%".

Explanation:

\text{MV of equity} = \text{equity price}  \times \text{number of outstanding shares}

                     =84 \times 4100000\\\\=344400000

\text{MV of Bond1}=\text{Par value} \times \text{bonds outstanding} \times \text{age of percentage}

                      =1000 \times 70000 \times 0.98 \\\\=68600000

\text{MV of Bond2}=\text{Par value} \times \text{bonds outstanding} \times \text{age of percentage}

                      =1000 \times 50000 \times 1.08 \\\\=54000000

\text{MV of firm} = \text{MV of Equity} + \text{MV of Bond1}+ \text{MV of Bond 2}

                  =344400000+68600000+54000000\\\\=467000000

\text{Weight of equity W(E)} = \frac{\text{MV of Equity}}{\text{MV of firm}}

                                     = \frac{344400000}{467000000}\\\\=0.7375

\text{Weight of debt W(D)}= \frac{\text{MV of Bond}}{\text{MV of firm}}

                                  = \frac{122600000}{467000000}\\\\=0.2625

Equity charges

By DDM.  

\text{Price = new dividend} \times  \frac{(1 + \text{rate of growth})}{( \text{Equity expense-rate of growth)}}

84 = 3.95  \times  \frac{(1+0.05)}{(\text{Cost of equity}- 0.05)}\\\\84 = 3.95  \times  \frac{(1.05)}{(\text{Cost of equity} - 0.05)}\\\\84 = \frac{4.1475}{ (\text{Cost of equity} - 0.05)}\\\\\text{Cost of equity} -0.05 = \frac{4.1475}{84}\\\\\text{Cost of equity} -0.05 = 0.049375\\\\\text{Cost of equity}  = 0.049375 + 0.05\\\\\text{Cost of equity}  = 0.099375 \\\\\text{Cost of equity} \%  = 9.9375 \% \ \ \ or  \ \ \ 9.94 \%  \\\\

Debt expenses  

Bond1

K = N \times 2 \\\\

Bond \ Price = \sum  [ \frac{\text{(Semi Annual Coupon)}}{(1 + \frac{YTM}{2})^k}]     +   \frac{Par\  value}{(1 + \frac{YTM}{2})^{N \times 2}}

k=1\\\\K =20 \times 2\\\\980 = \sum  [ \frac {(5.1 \times \frac{1000}{200})}{(1 + \frac{YTM}{200})^k}] +   \frac{1000}{(1 + \frac{YTM}{200})}^{20 \times 2}\\\\k=1\\\\\ YTM1 = 5.2628923903\\\\Bond2\\

K = N \times 2

Bond \ Price = \sum  [ \frac{\text{(Semi Annual Coupon)}}{(1 + \frac{YTM}{2})^k}]     +   \frac{Par\  value}{(1 + \frac{YTM}{2})^{N \times 2}}

k=1\\\\K =12 \times 2\\\\

1080 =\sum [\frac{(5.6 \times \frac{1000}{200})}{(1 + \frac{YTM}{200})^k}] +\frac{1000}{(1 +\frac{YTM}{200})^{12 \times 2}} \\\\k=1\\\\YTM2 = 4.72\\\\

\text{Company debt costs} = YTM1 times \frac{(MV \ bond1)}{(MV \ bond1+MV \ bond2)}+YTM2 \times \frac{(MV \ bond2)}{(MV \ bond2)}\\\\

The cost of the debt for the company:

= 5.2628923903 \times \frac{(68600000)}{(68600000+54000000)}+4.72 \times \frac{(68600000)}{(68600000+54000000)}\\\\

Business debt cost=5.02 \% \\\\

after taxation cost of debt:  

= \text{cost of debt} \times (1- tax \ rate)\\\\= 5.02 \times (1-0.21)\\\\= 3.9658\\\\

WACC= \text{after debt charges} \times W(D)+equity cost  \times W(E) \\\\

            =3.97 \times 0.2625+9.94 \times 0.7375 \\\\ =8.37 \% \\\\

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Data is not transmitted to a day center but rather being processed by the device itself or the server. It helps in bringing data storage and computation closer to the data sources and this helps in saving bandwidth and improving response times.

Since the company wants to improve its operations by using data from devices at individual locations to make real-time adjustments to service delivery, then the technology that would be combine with its current Cloud operations to make this possible is the edge computing.

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2 years ago
Mickey and Jenny Porter file a joint tax return, and they itemize deductions. The Porters incur $3,350 in investment expenses. T
wolverine [178]

Answer:

Investment interest expense deduction is restricted to the extent of investment income.

Investment interest expense deduction = $4600

Explanation:

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Answer:

Sunk cost = WDV of old machinery costing $431,000 - Any amount recovered.

Explanation:

Sunk cost is the cost that has actually been incurred and can not be avoided in any manner, currently while making both the decisions whether to buy model 220 machine or 370 machine we incurred the cost of dropping the old machinery of value of $431,000.

Therefore the book value of old machinery costing $431,000 is the sunk cost incurred in making the decision of buying new model.

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