Exercise 1. Management at Smokey Kettle, a loading Canadian manufacturer of maple syrup, is trying to control its inventory costs. The weekly cost of holding one \"unit\" of inventory is $30 (one unit is 1,000 cans of syrup). Tho marketing department estimates that weekly demand averages 120 units, with a standard deviation of 15 units, and is reasonably well modeled by a normal distribution. if demand exceeds the amount of syrup on hand, these sales are lost, that is, there is no bsrogging of demand. The production department can produce at one of three levels: 110, 120, or 130 units per week. The cost of changing production from one week to the next is $3,000. Management would like to evaluate the following production policy. 1f the current in- ventory is less than L = 30 units, then produce 130 units in the next week. If the current inventory is greater than U = 80 units, then produce 110 units in the next week. Otherwise, continue at the previous week's production level. Smokey Kettle currently has 00 units of inventory on hand. Last week's production level was 120. (a) Use a simulation of 1,000 trials to estimate the 52-week cost with values of U ranging from 30 to 80 in increments of 10. Keep L = 30 for every trial. (b) IConstruct 95% condence intervals for the mean 52-week cost for each of the six dif- ferent policies above (values of U}. What is the best value of U for L = 30'? Why? (c) For the best value of U identied above, what are the chances that the 52-week cost will exceed $120,000 in a year? Construct a 99% condence interval around this probability