Dr. tarun gupta, a michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. tarun can shoot a dog every 4 minutes. it is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 5 minutes according to a poisson distribution. also assume that taruna's shooting times are exponentially distributed. compute the following: a) the probability that tarun is idle. b) the proportion of the time that tarun is busy. c) the average number of dogs being vaccinated and waiting to be vaccinated. d) the average number of dogs waiting to be vaccinated. e) the average time a dog waits before getting vaccinated. f) the average amount of time a dog spends waiting in line and being vaccinated.

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The production manager of rordan corporation has submitted the following quarterly production forecast for the upcoming fiscal year: 1st quarter 2nd quarter 3rd quarter 4th quarter units to be produced 10,800 8,500 7,100 11,200 each unit requires 0.25 direct labor-hours, and direct laborers are paid $20.00 per hour. required: 1. prepare the company’s direct labor budget for the upcoming fiscal year. assume that the direct labor workforce is adjusted each quarter to match the number of hours required to produce the forecasted number of units produced. 2. prepare the company’s direct labor budget for the upcoming fiscal year, assuming that the direct labor workforce is not adjusted each quarter. instead, assume that the company’s direct labor workforce consists of permanent employees who are guaranteed to be paid for at least 2,500 hours of work each quarter. if the number of required direct labor-hours is less than this number, the workers are paid for 2,500 hours anyway. any hours worked in excess of 2,500 hours in a quarter are paid at the rate of 1.5 times the normal hourly rate for direct labor.