Math 135 Group Work #9 Spring 2009
Problem 1. For each function below, find fx,fy,fxx:
(a):
f(x, y) = 3x7y4
−2x√y
(b):
f(x, y) = ey2+xy
(c):
f(x, y) = (x−2y)11 ln y
Problem 2. A student with an 8 AM class at Cal State Fullerton commutes to school
by car. She has discovered that along each of two possible routes her travelling time
to school is approximately a normal random variable. If she uses the freeway, her
average driving time is 25 minutes with a standard deviation of 5 minutes. On the
other hand, if she uses surface streets, her average driving time is 28 minutes with a
standard deviation of 3 minutes.
(a): If she leaves home everyday at 7:30 AM, which route should the student take to
increase the likelihood that she’ll make it to class on time?
(b): Suppose instead that she leaves home everyday at 7:26 AM each day. Now which
route should the student take to increase the likelihood that she’ll make it to class
on time?
Problem 3. A company manufactures and sells two products, hand-held mirrors
and vases. The mirrors sell for $10 each, and the vases sell for $9 each. The cost of
producing and selling xmirrors and yvases is
C(x, y) = 400 + 2x+ 3y+ 0.01(3x2+xy + 3y2).
Find the values of xand ythat maximize the company’s profits.