Question1. .Each unit in a 10-unit population returns for service at an average interval of 20 minutes. If the cost of waiting is $32 per hour per unit and the cost of service is $50/T per unit per hour, find the optimum service time if there are two service channels. Assume Poisson arrivals and exponential service times.

Question 2. A population of 30 chemical processing units is to be sampled by a two-person crew. The mean time between calls for this operation is 68 minutes. If the mean service rate is one unit per minute, the cost of the crew and instruments will be $16 per minute. This cost will decrease to $12, $9, and $7 for service intervals of 2, 3, and 4 minutes, respectively.The time between calls for service and the service duration are distributed exponentially. If lost profit is $28 per hour for each unit that is idle, find the minimum cost service interval