For a fluid injection company, quantity injected per container is approximately normally distributed with a mean of 10 units and standard deviation .2 units. Each unit of fill costs $20 per unit. if a container contains less than 10 units (underfilled), it must be reprocessed at a cost of $10. A properly filled container sells for $230.
A container is initially underfilled and must be reprocessed. upon refilling, it contains 10.6 units. How much profit will the company make on this container? If the operations manager adjust the mean of the filling process upward to 10.5 units in order to make the probability of underfilling approximately 0 what would be the expected profit per container? Under these conditions, what is the expected profit per container?