QUESTION $4$

$[14$ MARKS$]$

A hotel approached Television Ltd to give a quotation for maintaining $100$ colour TV sets. The company's management must now decide how it will maintain these sets. Television Ltd currently has idle capacity and can maintain the $100$ sets using its own labour and parts. Management knows from experience with similar jobs that if only a few problems are encountered, the company's technicians can do the job for N $$8000.$ The probability of only encountering a few problems is $0\mathrm{.}2.$ However, if more problems are encountered, the maintenance cost is expected to increase to N$$18000.$

Television Ltd sometimes uses subcontractors to assist them with maintenance. Subcontractor A has quoted a fixed price of N $$17000,$ which includes labour and parts, to service the $100$ television sets.For $N$$$15000,$ Subcontractor B will supply the necessary parts. He will service the first $100$ calls free of charge and all calls thereafter at $N$$$40$ per call. The number of calls is expected to be as follows:

$\backslash$table$[[$Number of calls,Probability$],[100,50\%$