Quiz 14: Simulation 

Business

Calculate the benefit cost ratio of the project, as shown below: Step1: Estimate the total of benefits accruing from the projects as shown under: img The average or the most likely event is taken as the mean of the benefit for each criterion. Sum of the benefits is the total of the benefit from each 6 criteria's. Step2: Estimate the total costs in undertaking the project, as shown below: img The total cost is the sum of the cost accruing from each operational and maintenance source. Step3: Calculate the Benefit cost ratio by using the formula, as shown below: img B/C ratio = 25,915,800/19,040,500 B/C ratio = 1.361 Step 5: Estimate the probability of the Benefit cost ratio greater than 1, is shown as below: P (x = 1) img =-2.48 Calculate the probability for the given z value table. The probability for z 2.48 is 0.4934. Thus, the probability of benefit cost ratio greater than 1 = 0.493+0.5 = 0.993

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To determine the loss of revenue due to machine break down, using simulation is shown as follows: Step 1: Develop the probability distribution for machine repair time, as shown below: img Continuous probability function for time between breakdowns is given as: img Here, x = time between machine breakdown The equation for generating x, given random number r for the probability distribution is: img …… (1) Here, x = time between machine breakdown r= random numbers Also, the z (loss of revenue from the repair) is given by: img …… (2) Here, z= function of loss r= random number Step 2: Generate the random numbers for the break down and repair time as shown below: img Generate the random numbers by entering the formula in the cell as =RAND ( ) and calculate for both breakdown and repair time. x (breakdown time) is calculated using the formula in equation (2), which is as follows: x = 6 img vr =6 img v0.45 =4.03 Similarly, calculate the values for all the random variable. Calculate y (repair time) from the cumulative probability, i.e. Random number 61 lies in the range of 21-65 which has the repair time as 2. Step3: Obtain the random numbers for the loss accruing from the breakdown, as shown below: img As per the repair time in days, the random numbers are generated for each day. Such that for 2 days of repair time there are 2 random numbers associated with it. For repair time as 2, calculate the value of z using equation (2) as follows: z = 6r+2 =6 img 0.19 +2 = 3.14 z = 6 img 0.65+2 =5.90 Thus, the cumulative of the loss from the breakdown is 9.04 (3.14+5.09). Similarly the loss for each random number is calculated. Step4: Derive the total loss of revenue due to the machine break down, as shown below: img Thus, since the loss from the revenue is greater than 12,000 they should purchase a backup copier machine.

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