Reference no: EM132223434

1. The Mayflower Manufacturing Company produces a product on a number of machines. When a machine breaks down, it must be repaired; and it takes either one, 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: f (x) = x/18; 0 < x<6 weeks; where x = weeks between machine breakdowns. The reduced repair time resulting from the maintenance program is defined by the following discrete probability distribution: Machine Repair Time (y days) Probability of Repair Time (P(y)) 1 0.40 2 0.50 3 0.10 7 PBA4804 OCTOBER/NOVEMBER 2018 PORTFOLIO EXAMINATION [TURN OVER] Table 2, below 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. Table 2: Spreadsheet simulation model of the breakdown and repair processes (a) Derive an equation for generating x given the random number r. (b) Write down the formula for determining X in the spreadsheet cell D113. (c) What is the average time between breakdowns over the last four breakdowns in the simulation run? (d) What is the expected machine repair time resulting from the maintenance program? (e) What is the repair time of the 100th breakdown in the simulation run? (f) What is the repair cost of the 100th breakdown in the simulation run? 8 PBA4804 OCTOBER/NOVEMBER 2018 PORTFOLIO EXAMINATION [TURN OVER] (g) What is the input range for creating the descriptive statistics in the spreadsheet? (h) Use the descriptive statistics to draw conclusions about the characteristics of the probability distribution of the output variable of the simulation. (i) Calculate the lower limit of a 95% confidence interval for the cost.