The Mayflower Manufacturing Company produces a product on a number of machines. When a machine breaks down, it must be repaired; and it takes one, either two or three days for the repair to be completed. Every time a machine breaks down, the cost to the company is an estimated R2 000 per day in lost production until the machine is repaired.

The company would like to know if it should implement a machine maintenance program at a cost of R20 000 per year that would reduce the frequency of breakdowns and thus the time for repair. The maintenance program would result in the following continuous probability function for time between breakdowns:

fx= x18, 0x6, where x = weeks between machine breakdowns.

The reduced repair time resulting from the maintenance program is defined by the following discrete probability distribution:

Table 1: Repair Time Distribution

Machine Repair Time y (days))	Probability of Repair Time (P(y))
1	0.40
2	0.50
3	0.10

Table 2 (next page), represents a spreadsheet simulation model of the breakdown and repair processes in the maintenance program and the resulting costs. The spreadsheet is frozen at row 24 to show the first 10 breakdowns and the last 4.

(g) What is the input range for creating the descriptive statistics in the spreadsheet? (1 mark)

(h) Use the descriptive statistics to draw conclusions about the characteristics of the probability

distribution of the output variable of the simulation. (3 marks)

1 2 3 4 5 6 7 8 9 4,05 10 11 12 13 14 15 16 17 18 19 20 21 22 23 110 111 112 113 A B D H 1 Mayflower Manufacturing Company Machine Breakdown Simulation Model Repair Time Cum () 1 Average timewtwon brakdowns weeks 1 0,40 0,40 Average repair time 1,75 2 0,50 0,90 Average annual cost 44504.74 3 0,10 1,00 Cost (Rand) Time Mean 3500 Between Cum Repair StError 128,314 Breakdown RNI Beakdowns Time RN2 Time (Rand) Median 4000 Mode 4000 1 0,45 4,03 4,03 0,19 1 2000 Std Dev 1283,146 2 0,90 5,69 9.72 0,93 3 6000 Variance 1646464 3 0,84 5,50 15.22 0,65 2 4000 Kurtosis -0,6573 4 0,17 2.47 17,69 0,51 2 4000 Skewness 0,2781 5 0,74 5,16 22.85 0,63 2 4000 Rang 4000 6 0,94 5,82 28,67 0.17 1 2000 Minimum 2000 7 0,07 1,59 30,26 0,85 2 4000 Maximum 6000 8 0,15 2,32 32,58 0,37 1 2000 Sum 350000 9 0,04 1,20 33,78 0,89 2 4000 Count 100 10 0,31 37,12 0,76 2 4000 97 0,00 353,360,71 2 4000 og 0,99 5,97 389,33 0,11 1 2000 0.97 5,91 395,24 0,27 1 2000 100 0,73 400,37 0,41 Y Z 1 2 3 4 5 6 7 8 9 4,05 10 11 12 13 14 15 16 17 18 19 20 21 22 23 110 111 112 113 A B D H 1 Mayflower Manufacturing Company Machine Breakdown Simulation Model Repair Time Cum () 1 Average timewtwon brakdowns weeks 1 0,40 0,40 Average repair time 1,75 2 0,50 0,90 Average annual cost 44504.74 3 0,10 1,00 Cost (Rand) Time Mean 3500 Between Cum Repair StError 128,314 Breakdown RNI Beakdowns Time RN2 Time (Rand) Median 4000 Mode 4000 1 0,45 4,03 4,03 0,19 1 2000 Std Dev 1283,146 2 0,90 5,69 9.72 0,93 3 6000 Variance 1646464 3 0,84 5,50 15.22 0,65 2 4000 Kurtosis -0,6573 4 0,17 2.47 17,69 0,51 2 4000 Skewness 0,2781 5 0,74 5,16 22.85 0,63 2 4000 Rang 4000 6 0,94 5,82 28,67 0.17 1 2000 Minimum 2000 7 0,07 1,59 30,26 0,85 2 4000 Maximum 6000 8 0,15 2,32 32,58 0,37 1 2000 Sum 350000 9 0,04 1,20 33,78 0,89 2 4000 Count 100 10 0,31 37,12 0,76 2 4000 97 0,00 353,360,71 2 4000 og 0,99 5,97 389,33 0,11 1 2000 0.97 5,91 395,24 0,27 1 2000 100 0,73 400,37 0,41 Y Z