Problem $1(5$ Points$)$: A plant engineer is about to commence an urgent above normal production rin. To ensure meeting the desired production rate, she has decided to transfer and incorporate into the production line a piece of equipment from another line at a cost of $$6000.$ The engineer is considering whether to overhaul this equipment before placing it in the new production line The piece of equipment costs $$1000$ to overhaul, whereas if she incorporates the item into the process line and it then breaks down it will cost $$1200$ to cover the cost of repair and lost time. The engineer estimates that there is a $70\%$ chance that the equipment motor is relable but is assured that it will be reliable if it is overhauled. A dynamometer test of the motor costs $$150$ but will only indicate whether the motor is in good or bad condition with a $15\%$ chance that the test results prove invalid. The engineer estimates that there is a $80\%$ chance that the dynamometer test will indicate a reliable motor. If the plant manager wishes to base ber decision on expected monetary value, what should be her optimum strategy?