3. A job shop consists of three machines and two repairmen. The amount of time a machine works before breaking down is exponentially distributed with mean 10. If the amount of time it takes a single repairman to fix a machine is exponentially distributed with mean 8 , then (a) what is the average number of machines not in use? (b) what proportion of time are both repairmen busy? (5 points) Do Problem 6.23, page 424 in the text. Also compute (c), the long-run average profit per unit time if each repairman earns a salary of $s per unit time (regardless of whether he/she is working) plus a bonus $b per completed repair, each working machine produces value $v per unit time, and there is an operating cost of $cw($cf) per unit time for each working (failed) machine (not including the repairmen's salary). Explain