Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist enter DNE.)f(x, y) = 5x + y +2 with constraint g(x, y) = xy = 1

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.

Donald has x twenty-dollar bills and 11 ten-dollar bill. how much money does donald have? write your answer as an expression.

One of every 20 customers reports poor customer service on your company’s customer satisfaction survey. you have just created a new process that should cut the number of poor customer service complaints in half. what percentage of customers would you expect to report poor service after this process is implemented? 1.) 5% 2.) 10% 3.) 2% 4.) 2.5%