Applications - A Guide to MATLAB for Beginners and Experienced Users - page 208

quarter from those in Metropolis, a half-dollar from the Oz resi-
dents, and three bucks from the folks in River City. She must raise
at least $10,000 from her entire canvass.
Jane's goal is to maximize the number of supporters (those likely to
vote for her). She estimates that for each residence she visits in Gotham
the odds are 0.6 that she picks up a supporter, and the corresponding
probabilities in Metropolis, Oz, and River City are, respectively, 0.6, 0.5,
and 0.3.
(a) How many residences should she visit in each of the four cities?
(b) Suppose she can double the time she can allot to visits. Now what
is the profile for visits?
(c) But suppose that the extra time (in part (b)) also mandates that she
double the contributions she receives. What is the profile now?
9. Consider the following linear programming problem. The famous football
coach Nerv Turnip is trying to decide how many hours to spend with each
component of his offensive unit during the coming week — that is, the
quarterback, the running backs, the receivers, and the linemen. The con-
straints are as follows:
(i) The number of hours available to Nerv during the week is 50.
(ii) Nerv figures he needs 20 points to win the next game. He estimates
that for each hour he spends with the quarterback, he can expect
a point return of 0.5. The corresponding numbers for the running
backs, receivers, and linemen are 0.3, 0.4, and 0.1, respectively.
(iii) In spite of their enormous size, the players have a relatively thin
skin. Each hour with the quarterback is likely to require Nerv to
criticizehimonce.Thecorrespondingnumberofcriticismsperhour
for the other three groups are 2 for running backs, 3 for receivers,
and 0.5 for linemen. Nerv figures he can only bleat out 75 criticisms
in a week before he loses control.
(iv) Finally, the players are prima donnas who engage in rivalries. Be-
cause of that, he must spend the exact same number of hours with
the running backs as he does with the receivers, at least as many
hours with the quarterback as he does with the runners and re-
ceivers combined, and at least as many hours with the receivers as
withthe linemen.
Nerv figures he's going to be fired at the end of the season regardless
of the outcome of the game, so his goal is to maximize his pleasure during
the week. (The team's owner should only know.) He estimates that, on a
sliding scale from 0 to 1, he gets 0.2 units of personal satisfaction for each