A factory produces x packs of pencils and y packs of pens each day. • The factory can produce no more than a total of 50 packs of pens and pencils each day.
• At least 10 packs of pencils are produced each day.
• At least 20 packs of pens are produced each day.
• The company makes $0.25 on a pack of pencils and $0.50 on a pack of pens.
What are the vertices of the feasible region for the system of inequalities that models the constraints?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.