Problem 1: America creates more garbage than any other nation. According to Denis Hayes, president of Seattle's nonprofit Bullitt Foundations and a founder of Earth Day, "We need to be an Heirloom Society instead of a Throw-Away Society." The EPA estimates that, on average, we each produce 4.4 pounds of garbage daily (Source: Take out the Trash, and put it _where?" by Bernard Bavzer, Parade Magazine, June 13, 1999). The following graph illustrates the annual production of municipal solid waste in the U.S. for the years listed.
a) Model the data with two linear functions. Let the independent variable represent the number of years after 1960.
b) With each function found in part a), predict the amount of municipal solid waste in 2005.
c) Which of the two models appears to fit the data more closely (the more realistic prediction)?
Problem 2. The waste hauling company profits are stated as the difference between revenue and costs. That is P(x) = R(x) - C(x), where x is the number of tons processed. Find the maximum profit and the number of tonnage which must be processed in order to yield the maximum profit for each of the following:
a) R(x) = 5x; C(x) = 0.0001x2 + 1.2x + 60.
b) R(x) = 50x - 0.5x2; C(x) = 10x + 3.
c) R(x) = 20x - 0.1x2; C(x) = 4x +2.