Your mathematics club has arranged to earn some extra money by cleaning up Carr Park. The City Recre-
ation Department agrees to pay each old member $10 and each new
member $8 for their services. (The club did the same thing last year,
so the old members are experienced.)
a. Define variables, then write an equation expressing the dollars
the club earns in terms of the numbers of old and new members
who work.
b. The following facts restrict the numbers of students who can
work:
i. The number of old members is non-negative, and so is the
number of new members.
ii. The club has at most 9 old members and at most 8 new
members who can work.
The Department will hire at least 6 students, but no more
than 15.
iv. There must be at least 3 new members.
The number of new members must be at least 1/2 the num-
ber of old members, but less than 3 times the number of
old members.
Write inequalities for each of the above requirements.
c. Draw a graph of the solution set of this system of inequalities.
Remember that club members come only in integer quantities!
d. Based on your graph, is it feasible to do without any old mem-
bers at all? Explain.
e. Shade the portion of the feasible region in which the club would
make at least $100.
f. Draw a line on the graph showing the number of old and new
members needed to make $160. Is it feasible to make $160? Ex-
plain.
What numbers of old and new members would earn the maxi-
mum feasible amount? What would this amount be?
h. What is the minimum feasible amount the club could earn?
i. Suppose tradition was broken and the new members were paid
more than the old members. What would be the maximum feasi-
ble earnings if new members get $12 and old members get $10?