Problem 1.[10 points] If inputs increase by 32%, and outputs decrease by 20%, what isthe percentage change in productivity?Problem 2.[20 points] Suppose that a firm is considering opening a plant on the moon,and the current exchange rate is 580 moon pieces (mp) per dollar. Also, the wage rate is9,280 mp per hour. Suppose further that U.S. workers can produce 220 units per hour, whileworkers on the moon are expected to be able to produce 300 units per hour (the lower gravitylevel helps them work faster).(a) What is the relative wage rate (in dollars, rounded to the nearest penny) of oper-ating on the moon, after taking productivity differences into account?(b) Suppose that the U.S. wage rate is$13.50 per hour. If the U.S. managers want tobecome the location of choice for production, and if they cannot lower their wagerate due to labor union agreements, what does the labor productivity in the U.S.need to become (rounded to one decimal place)?Problem 3.[20 points] Assume a system has one component, and the reliability of thiscomponent is 98.5%. Further assume, it will cost$80 to fix the system when the componentfails.(a) What is the expected fixing cost per part?(b) If a backup with the same reliability can be installed at a cost of$1.00 per part,should the backup be installed?