Recall the model
d
x
d
t
=
a
x
+
b
y
d
y
d
t
=
c
x
+
d
y
for Paul's and Bob's cafés, where
x
(
t
)
is Paul's daily profit,
y
(
t
)
is Bob's daily profit, and $a, b, c,$ and
d
are parameters governing how the daily profit of each store affects the other. In Exercises
1
−
4
,
different choices of the parameters $a, b, c,$ and
d
are specified. For each exercise write a brief paragraph describing the interaction between the stores, given the specified parameter values. [For example, suppose
a
=
1
,
c
=
−
1
,
and
b
=
d
=
0.
If Paul's store is making a profit
(
x
>
0
)
,
then Paul's profit increases more quickly (because
a
x
>
0
). However, if Paul makes a profit, then Bob's profits suffer (because
c
x
<
0
). since
b
=
d
=
0
,
Bob's current profits have no impact on his or Paul's future profits.]
1.
a
=
1
,
b
=
−
1
,
c
=
1
,
and
d
=
−
1