A complex airborne navigating system incorporates a sub$-$assembly which unrolls a map of the flight plane synchronously with the movement of the aero$-$plane. This sub$-$ assembly is brought on very good terms from the sub$-$contractor $,$ but is not always in perfect adjustment on delivery $.$ The sub$-$assemblies can be re adjusted on to guarantee at the cost of SR $500$ per sub$-$assembly $.$ It is not, however, possible to distinguish visually those sub$-$assemblies that need adjustment. Alternatively $,$ the sub$-$assemblies can each be tested electronically at a cost of SR$100$ per sub$-$assembly tested. Past experience shows that about $30\%$ of those supplied are defective, the probability of the test indicating a bad adjustment when the sub$-$assembly is faulty is $0\mathrm{.}8,$ while the probability that the test indicates a good adjustment when the sub$-$assembly is properly adjusted is $0\mathrm{.}7.$ If the adjustments is not made and the sub$-$assembly is found to be faulty when the system has its final check, the cost of subsequent rectification will be Sr$1400.$ Draw up an appropriate decision tree to show the alternatives open to the purchaser and use it to determine his appropriate course of action. Draw rhe decision tree.