CHAPTER 8 EXERCISES
1. (a) The results of Step 1 are summarized in Figure 1.
Variables:
Sn = supply of aquariums at the
beginning of week n
Dn = demand for aquariums during
week n
Assumptions:
If Dn1 + 1 < Sn1 , then Sn = Sn1 Dn1
If Dn1 + 1 Sn1 , then Sn

CHAPTER 6 EXERCISES
1. (a) The following graph shows the results of a simulation of the model with lambda=3
and w=0.25, starting with 2 blue and 5 red divisions. Red wins the battle in 39 hours with
2.2 divisions remaining.
2
b
l
1
u
e
0
0
1
2
3
4
5
red
(

CHAPTER 7 EXERCISES
1. (a) Compute
A (x) = 4/x2 5 ln(0.997)(0.997)x
A (x) = 8/x3 5 ln(0.997)2 (0.997)x
and notice that A (x) < 0 for any x > 0 so that A (x) is increasing on x > 0.
Then the unique point x = x0 where A (x0 ) = 0 is the global maximum
of A(