Management of Ebony, a leading manufacturer of bath soap, is trying to control its inventory costs.The weekly cost of holding one unit of soap in inventory is $30 (one unit is 1000 cases of soap).The 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 soap on hand, those sales are lostthat is, there is no backlogging of demand.The production department can produce at one of three levels: 110, 120, or 130 units per week.The cost of changing the production level from one week to the next is $3000. Management would like to evaluate the following production policy. If the current inventory is less than L = 30 units, they will produce 130 units in the next week. If the current inventory is greater than U = 80 units, they will produce 110 units in the next week. Otherwise, Ebony will continue at the previous week's production level. Ebony currently has 60 units of inventory on hand. Last week's production level was 120. Develop a simulation model for 52 weeks of operation at Ebony. Graph the inventory of soap over time.What is the total cost (inventory cost plus production change cost) for the 52 weeks