Golf Course Design

This document discusses the process of designing a golf course and constructing a clubhouse. It explores different options and constraints involved in the project, such as the number of holes, the type of holes, the size and cost of the clubhouse, and the total project budget. The objective is to maximize the enjoyment index of the clients while staying within the given constraints.

Action Plan
1. Identification if the decision variables.
In the models developed above the decision variables are the number of golf holes that
need to be constricted. In this case this will be defined by letters k’s with the number of
holes constructed defined as illustrated below.
k1 =number of straight par 5
k 2=number of dogleg par 5
k3 =number of straight par 4
k 4=number of dogleg par 4
k5 =Long par 3
k 6=short par 3
2. Identification of the objective function
The objective of the linear programming is to maximise the total utility of the clients.
This will be modelled by maximising the total enjoyment index derived from the golf
holes and the clubhouse constructed.
3. Identification of the constraints
The constraints for the project are classified into two; first we have the resource
constraints. These are
The total project cost should not exceed $ 20 million
The total land area covered by the project ought to be between 36 and 42 hectares.
Second, we have the constraint that are as a result of the minimum features that need to
be met for the golf resort to be classified as an international resort. The constraints in this
area are
Straight par 5 holes should not be less than 1
Dogleg par 5 holes should not be less than 1
Straight par 4 holes should not be less than 2
Dogleg par holes should not be less than 2
Long par holes should not be less than 1
Short par holes should not be less than 1
The total par 5 should not exceed 4

The total par 4 should not exceed 14
The total par 3 should not exceed 4
Total pars should be between 70 and 72
The golf holes should be 18 in total
4. Writing the objective function and the constraints as mathematical formulas
This will be done for each of the models developed as the information varies from model
to model. The clubhouse will be represented by z as explained below.
z1=Standard clubhouse
z2=Exclusive clubhouse
Standard clubhouse model
This entails construction of a standard clubhouse occupying 2 hectares at a cost of $ 3.5
million inside the golf resort.
Max ; 2 k1+1.5 k2+1.5 k3+ 2 k4 +1.75 k5 +2.25 k6
Under the constraints
1000000 k1 +1500000 k2 +750000 k3 +900000 k4 + 600000 k5+ 650000 k6 +3500000 z1 ≤20000000
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +2 z1 ≤ 42
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +2 z1 ≥ 36
5 k1 +5 k2 + 4 k3 + 4 k4 + 3 k5 +3 k6 ≤72
5 k1 +5 k2 + 4 k3 + 4 k4 +3 k5 +3 k6 ≥70
k1 ≥ 1
k 2 ≥ 1
k3 ≥ 2
k 4 ≥ 2
k5 ≥ 1
k 6 ≥ 1
k1 + k2 ≤ 4
k3 + k4 ≤14
k5 + k6 ≤ 4
The excel output is as summarised below.

Golf Course Design
Kind of golfing hole Par Size taken up by the holes Enjoyment Index Building Cost Number of holes
Straight Par 5 5 3 2 $1,000,000 1 >= 1
Dogleg Par 5 5 3.5 1.5 $1,500,000 1 >= 1
Straight Par 4 8 4 3 $1,500,000 2 >= 2
Dogleg Par 4 40 25 20 $9,000,000 10 >= 2
Long Par 3 3 1 1.75 $600,000 1 >= 1
Short Par 3 9 2.25 6.75 $1,950,000 3 >= 1
Clubhouse
Standard
Cost $3,500,000
Size 2
Objective Function
Total Enjoyment Index 35
Constraints
Total project coverage 40.75 >= 36
Total project coverage 40.75 <= 42
Total project Cost $19,050,000 <= $20,000,000
Par 5 2 <= 4
Par 4 12 <= 14
Par3 4 <= 4
Total Pars 70 <= 72
Total Pars 70 >= 70
Golf holes 18 = 18
Exclusive clubhouse model
The model entails construction of a 4-hectare excusive warehouse inside the golf resort at
a cost of $ 6 million.
Max ; 2 k1+1.5 k2+1.5 k3+ 2 k4 +1.75 k5 +2.25 k6 + 4 z2
Under the constraints
1000000 k1 +1500000 k2 +750000 k3 +900000 k4 + 600000 k5+ 650000 k6 +6000000 z2 ≤ 20000000
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≤ 42
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≥ 36
5 k1 +5 k2 + 4 k3 + 4 k4 + 3 k5 +3 k6 ≤72
5 k1 +5 k2 + 4 k3 + 4 k4 +3 k5 +3 k6 ≥70
k1 ≥ 1
k 2 ≥ 1

k3 ≥ 2
k 4 ≥ 2
k5 ≥ 1
k 6 ≥ 1
k1 + k2 ≤ 4
k3 + k4 ≤14
k5 + k6 ≤ 4
This model has no feasible solution
Option 1
The exclusive clubhouse model is modified by reducing the area covered by the
clubhouse to 3.4 hectares.
Max ; 2 k1+1.5 k2+1.5 k3+ 2 k4 +1.75 k5 +2.25 k6 + 4 z2
Under the constraints
1000000 k1 +1500000 k2 +750000 k3 +900000 k4 + 600000 k5+ 650000 k6 +5400000 z2 ≤20000000
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +3.4 z2 ≤ 42
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +3.4 z2 ≥ 36
5 k1 +5 k2 + 4 k3 + 4 k4 + 3 k5 +3 k6 ≤72
5 k1 +5 k2 + 4 k3 + 4 k4 +3 k5 +3 k6 ≥70
k1 ≥ 1
k 2 ≥ 1
k3 ≥ 2
k 4 ≥ 2
k5 ≥ 1
k 6 ≥ 1
k1 + k2 ≤ 4
k3 + k4 ≤14
k5 + k6 ≤ 4
The model has no feasible solution

Option 2
Here the exclusive clubhouse is constructed at a cost of $ 5.1 million
Max ; 2 k1+1.5 k2+1.5 k3+ 2 k4 +1.75 k5 +2.25 k6 + 4 z2
Under the constraints
1000000 k1 +1500000 k2 +750000 k3 +900000 k4 + 600000 k5+ 650000 k6 +5100000 z2 ≤20000000
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≤ 42
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≥ 36
5 k1 +5 k2 + 4 k3 + 4 k4 + 3 k5 +3 k6 ≤72
5 k1 +5 k2 + 4 k3 + 4 k4 +3 k5 +3 k6 ≥70
k1 ≥ 1
k 2 ≥ 1
k3 ≥ 2
k 4 ≥ 2
k5 ≥ 1
k 6 ≥ 1
k1 + k2 ≤ 4
k3 + k4 ≤14
k5 + k6 ≤ 4
The model is summarised by the table below.

Kind of golfing hole Par Size taken up by the holes Enjoyment Index Building Cost Number of holes
Straight Par 5 10 6 4 $2,000,000 2 >= 1
Dogleg Par 5 5 3.5 1.5 $1,500,000 1 >= 1
Straight Par 4 28 14 10.5 $5,250,000 7 >= 2
Dogleg Par 4 16 10 8 $3,600,000 4 >= 2
Long Par 3 3 1 1.75 $600,000 1 >= 1
Short Par 3 9 2.25 6.75 $1,950,000 3 >= 1
Clubhouse
Exclusive
Cost $5,100,000
Size 4
Enjoyment Index 4
Objective Function
Total Enjoyment Index 36.5
Constraints
Total project coverage 40.75 >= 36
Total project coverage 40.75 <= 42
Total project Cost $20,000,000 <= $20,000,000
Par 5 3 <= 4
Par 4 11 <= 14
Par3 4 <= 4
Total Pars 71 <= 72
Total Pars 71 >= 70
Golf holes 18 = 18
Option 3
Under option 3, the golf resort construction budget is increased to $21 million.
Max ; 2 k1+1.5 k2+1.5 k3+ 2 k4 +1.75 k5 +2.25 k6 + 4 z2
Under the constraints
1000000 k1 +1500000 k2 +750000 k3 +900000 k4 + 600000 k5+ 650000 k6 +6000000 z2 ≤ 21000000
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≤ 42
3 k1 +3.5 k2 +2 k3 +2.5 k 4 +1 k5+ 0.75 k6 +4 z2 ≥ 36
5 k1 +5 k2 + 4 k3 + 4 k4 + 3 k5 +3 k6 ≤72
5 k1 +5 k2 + 4 k3 + 4 k4 +3 k5 +3 k6 ≥70
k1 ≥ 1
k 2 ≥ 1
k3 ≥ 2
k 4 ≥ 2
k5 ≥ 1
k 6 ≥ 1

k1 + k2 ≤ 4
k3 + k4 ≤14
k5 + k6 ≤ 4
The output is summarised below.
Kind of golfing hole Par Size taken up by the holes Enjoyment Index Building Cost Number of holes
Straight Par 5 5 3 2 $1,000,000 1 >= 1
Dogleg Par 5 5 3.5 1.5 $1,500,000 1 >= 1
Straight Par 4 24 12 9 $4,500,000 6 >= 2
Dogleg Par 4 24 15 12 $5,400,000 6 >= 2
Long Par 3 3 1 1.75 $600,000 1 >= 1
Short Par 3 9 2.25 6.75 $1,950,000 3 >= 1
Clubhouse
Exclusive
Cost $6,000,000
Size 4
Enjoyment Index 4
Objective Function
Total Enjoyment Index 37
Constraints
Total project coverage 40.75 >= 36
Total project coverage 40.75 <= 42
Total project Cost $20,950,000 <= $21,000,000
Par 5 2 <= 4
Par 4 12 <= 14
Par3 4 <= 4
Total Pars 70 <= 72
Total Pars 70 >= 70
Golf holes 18 = 18