24. The administrator for a large mid-western city continually seeks ways to reduce costs without cutting service. The administrator has asked all department heads to review their operations to determine if cost saving procedures can be implemented.

The Department of Streets is responsible for the proper functioning of the city's computerised traffic control system including the replacement of 50,000 bulb units in the traffic lights. The department has kept detailed records regarding the failure rate of the bulb units over the past 18 months. The pattern of bulb failures that has been experienced is as follows:

The Department of Streets has been replacing the bulb units as they have failed. The estimated cost to replace the bulb units, using this procedure, exclusive of the cost of the bulb unit, is Rs 5.40 per unit.
The manager of the Department of Streets is considering replacing all of the bulb units at once, for example, at the beginning of every quarter, plus replacing bulbs as they fail. The manager estimates that the cost to replace all bulb units at once would be Rs 1 .40 per unit, exclusive of the cost of the bulb. The cost to replace each unit as it failed would still be Rs 5.40 per unit.
Each bulb costs Re 1 regardless of the replacement procedure used.

(a) Calculate the annual bulb and replacement cost to the Department, if the present policy ofreplacing the bulb units as they fail is continued.

(b) Calculate the estimated annual bulb and replacement cost if all bulb units are replaced when they fail and all bulb units are replaced on a regular basis at the beginning of (i) every quarter, (ii) every second quarter, (iii) every third quarter. Show your calculations for all the three alternatives.
(

c) Why would there be such a large difference between the two estimated replacement costs per unit (replace as failure occurs, Rs 5.40; replace all at once, Rs 1 .40)? Explain your answer

Failure occurs within quarter of replacement First Second Third Probability 0.1 0.3 0.6