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## Simulation

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**Simulation**An Example**A garage hires out cars. It currently owns four cars which**are hired out on a daily basis for a number of days. The demand pattern in the past has been as follows**The company charges £40 a day for hire. It estimates that**the total fixed overheads attributed to this operation are £10 a day. If the car is hired out the extra repair and maintenance costs generated are estimated at £6 a car a day.**If the demand for hired cars exceeds the current number of**four cars they then hire from another garage at additional cost of £24 a day. Carry out a simulation to forecast the overall demand pattern for car hire and estimate the annual contribution to overheads and profits from the car hire business.**The first thing to do is to construct cumulative frequency**tables to decide which random numbers refer to a particular scenario.**This means, for example, that a random number of 17 would**interpret as a demand of 1 on that particular day, whilst a value of 95 would imply a demand of 4. The same process is carried out for length of hire.**We will use the following random numbers (from a book of**tables) 84 42 56 73 87 75 18 91 76 66 64 83 97 11 69 41 80 92 38 75 28 87 77 03 57 09 85 86 46 86 40 15 31 81 78 91 30 22 88 58 Generate 10 days of business**Day 1**• Random Number is 84 • This means a demand of 3**Day 1**• We now need to work out how long each car is out for**Length of Rental**• Car 1 • Next Random Number is 42 • This corresponds to a duration of 1 day**Length of Rental**• Car 2 • Next Random Number is 56 • This corresponds to a duration of 1 day • Car 3 • Next Random Number is 73 • This corresponds to a duration of 2 days**Day 2**• Random Number is 87 • This means a demand of 3**Length of Rental**• The next three random numbers are 75, 18 and 91 meaning rental durations of 2, 1 and 3 respectively**This can be carried on for a ten day period and the costs**calculated.