Bulb Replacement Problem: Lighting on exit ramp 167 on I-55 consists of a cluster of 3 bulbs. Safety regulations require that it must be immediately replaced whenever a bulb fails. The cost of the bulb is $450 per unit. The 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 bulbs life is described by the following probability distribution. Use only the random numbers provided. PLEASE INCLUDE FORMULAS

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 it must be immediately replaced whenever a bulb fails. The cost of the bulb is $450 per unit. The 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 WN The 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 0 Olo00 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 5 6 4 1 8 3 9 2 6 3 5 6 3 3 9 5 2 0 8 5 6 9 1 8 4 9 2 3 3 5 6 6 3 0 3 9 0 2 0 5 5 6 8 1 8 9 9 2 4 3 5 3 6 3 6 3 9 0 Alternative 2: Replace all three bulbs when one fails (Use these Random Numbers in sequence) Time Bulb 1 R# Bulb 2 R# Bulb 3 R# 0 2 8 1 6 2 8 4 6 4 9 1 1 3 6 1 8 3 6 9 1 4 9 4 9 5 2 8 1 6 2 8 0 4 9 1 1 3 6 1 9 8 3 6 9 1 4 4 9 4 9 0 9 6 5 2 8 1 4 9 8 3 6 1