Suppose a designer is to make a decision between two manufacturing processes for the manufacture of a certain component. Process A costs $100 per unit to manufacture a component. Process B costs $120 per unit to manufacture a component. Components have an exponential time to failure density with a failure rate 1/200 failures per hour for process A, while components from process B have a failure rate of 1/300 failures per hour. The mean lives are thus 200 hours and 300 hours, respectively, for the two processes. Because of a warranty clause, if a component lasts for fewer than 400 hours, the manufacturer must pay a penalty of $80. Calculate the expected cost for each process and determine which one should be preferred