How many months does it take rivals to copy and introduce their own new-and-improved version of a newly introduced product

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When a company produces and sells x thousand units per week, its total weekly profit is p thousand dollars, where upper p equals startfraction 800 x over 100 plus x squared endfraction . the production level at t weeks from the present is x equals 4 plus 2 t. find the marginal profit, startfraction dp over dx endfraction and the time rate of change of profit, startfraction dp over dt endfraction . how fast (with respect of time) are profits changing when tequals8?

Mountain mouse makes freeze-dried meals for hikers. one of mountain mouse's biggest customers is a sporting goods superstore. every 66 days, mountain mouse checks the inventory level at the superstore and places an order to restock the meals. these meals are delivered by ups in 55 days. average demand during the reorder period and order lead time is 8585 meals, and the standard deviation of demand during this same time period is about 1919 meals.calculate the restocking level for mountain mouse. assume that the superstore wants a 95\% service level. what happens to the restocking level if the superstore wants a higher level of service-say, 99]%? the restocking level for the 95% service level is 117 mealssuppose there are 25 meals in the superstore when mountain mouse checks inventory levels. how many meals should be ordered, assuming a 95% service level?