Question

The Quick Wash 24-hour Laundromat has 16 washing machines. A machine breaks down every 20 days (exponentially distributed). The repair service with which the Laundromat contracts takes an average of 1 day to repair a machine (exponentially distributed). A washing machine averages $5 per hour in revenue. The Laundromat is considering a new repair service that guarantees repairs in 0.50 day, but it charges $10 more per hour than the current repair service. Should the Laundromat switch to the new repair service?

Answer 1

`Hey,

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Repair service charge per hour by current service was not given in the data

So, based on current service repair charge the answer for this problem is like this

If currently service repair charge = $ 5 , both options are same. Any one can be choosen.

If currently service repair charge > $ 5,( 24 x > 12 x + 60), Laundromat should switch to the new repair service

if currently service repair charge < $ 5 ( 24 x < 12 x + 60), Laundromat should not switch to the new repair service

Explanation:

Let us assume $ x for repair washing machine bu current service

it takes one day= 24 hours, the, 24 x dollars to repair one machine.

By new service it takes 0.5 day = 12 hrs for repairing the machine

but repair price is $10 more per hour than the current repair service. Means charge = 10+x

By new service, for 12 hrs charge = 12(10+x) = $ 12x +120

As new service finishes in 0.5 day, remaining, 0.5 days (12 hours ) machine can work. A washing machine averages $5 per hour in revenue. So Revenue gain due to new service = 12 x5 = $ 60

By new service charge = $ 12x +120 and earning is $ 60

Net charge by new service in comparison to current service = $ 12x + $120 - $ 60 = $ 12x + $ 60

By current service repair charge = $ 24 x ...(1)

By new service, repair charge = $ 12x + $ 60 ...(2)

But repair charge per hour by current service (x) was not given in the data

make (1) = (2) then find x = ?

24 x = 12 x + 60

12 x =60

x = $ 5

If currently service repair charge = $ 5 , both options are same. Any one can be you can choose.

If currently service repair charge > $ 5,( 24 x > 12 x + 60), Laundromat should switch to the new repair service

if currently service repair charge < $ 5 ( 24 x < 12 x + 60), Laundromat should not switch to the new repair service

Kindly revert for any queries

Thanks.