An orange grove produces a profit of $ 94 per tree when there are 1100 trees planted. Because of overcrowding, the profit per tree (for every tree in the grove) is reduced by 5 cents per tree for each one additional tree planted. How many trees should be planted in order to maximize the total profit of the orange grove?

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.