The KLM Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each
ID: 428894 • Letter: T
Question
The KLM Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each year KLM allows retailers of Christmas trees to select and cut trees for sale to individual customers. KLM protects small trees (usually less than 4 feet tall) so that they will be available for sale in future years. Currently 1500 trees are classified as protected trees, while the remaining 3500 are available for cutting. However, even though a tree is available for cutting in a given year, it may not be selected for cutting until future years.
While most trees not cut in a given year live until the next year, some diseased trees are lost every year.
In viewing the KLM Christmas tree operation as a Markov process with yearly periods, we define the following four states:
State 1 Cut and sold
State 2 Lost to disease
State 3 Too small for cutting
State 4 Available for cutting but not cut and sold
The following transition matrix is appropriate:
State 1
State 2
State 3
State 4
P =
1.0
0.0
0.0
0.0
0.0
1.0
0.0
0.0
0.1
0.2
0.5
0.2
0.4
0.1
0.0
0.5
A) how many of the trees that are available for cutting but not cut and sold will eventually be lost to disease?
State 1
State 2
State 3
State 4
P =
1.0
0.0
0.0
0.0
0.0
1.0
0.0
0.0
0.1
0.2
0.5
0.2
0.4
0.1
0.0
0.5
Explanation / Answer
Let x1=no of trees cut and sold
x2=no of trees lost to disease
x3=too small for cutting=1500
x4=no of trees available for cutting but not cut and sold
initial system state S1={x1,x2,1500,x4}
given transition matrix
{1,0,0,0 }
{0,1,0,0 }
{0.1,0.2.0.5,0.2}
{0.4,0.1,0,0.5}
after solving using excel solver
x1=10498
x2=14497
x3=1500(already given)
x4=5498
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.