Question 3: (5 points) Service Management Bulb Replacement Problem: Lighting on exit ramp 167 on 1-55 consists of a cluster of 3 bulbs. Safety regulations require that whenever a bulb fails, it must be immediately replaced. Cost of the bulb is $450 per unit. Cost of making the trip to replace one or more bulbs is $900 (independent of the number of bulbs replaced). Based on past experience, a bulb's life is described by the following probability distribution. Use only the random numbers provided. Duration (life of bulb) in Probability Cumulative Probability months 2 0.2 3 0.3 4 0.3 5 0.2 Highway department wants to investigate two possible alternative policies- i) replace a bulb when it fails, or ii) replace all bulbs whenever one or more bulbs fail no matter when that bulb was installed. Simulate the system (alternative-1 for 25 months and alternative-2 for 25 months). A) Which policy the department should use. B) What is the optimum monthly average cost of operating the system? C) Can you suggest yet third alternative policy which may be worthwhile investigating? Time Alternative 1: Replace only bulb that fails (Use these Random Numbers in sequence) Bulb 1 Bulb 2 Bulb 3 R# R# R# 2 0 9 0 6 4 5 1 8 3 9 6 2 5 3 0 6 3 0 9 5 0 8 3 2 5 1 6 9 8 4 9 2 3 5 6 3 6 3 3 9 2 0 oloi 00 + 5 6 1 8 9 9 2 9 2 4 3 5 3 6 3 6 3 9 0 Simulate Alternative 1 for 25 months. Alternative 2: Replace all three bulbs when one fails (Use these Random Numbers in sequence) Time Bulb 2 R# Bulb 3 R# 8 0 4 Bulb 1 R# 2 8 1 6 9 3 6 1 1 9 2 3 1 6 8 4 4 9 1 6 4 9 5 0 9 4 8 2 8 9 3 B D E 1 6 1 6 1 9 OO NO 1 4 4 9 3 6 1 4 0 4 9 1 9 9 8 3 8 1 6 Simulate Alternative 2 for 25 months