Action Plan. Identity of the decision variables. The de

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Action Plan
1. Identity of the decision variables
The decision variables are the number of golf holes that need to be constructed for each
type of golf holes. In this case let the number of golf holes be represented by y and the
type of clubhouse by x; then
y1=Straight par 5
y2=Dogleg par 5
y3=Straight par 4
y4 =Dogleg par 4
y5=Long par 3
y6=Short par 3
x1=Standard clubhouse
x2=Exclusive clubhouse
2. Identity of the objective function
The objective of the firm is to optimise the enjoyment index. The objective function will
thus be the total enjoyment index that is derived from the clubhouse and the golf holes.
3. Model Constraints
The constrains are the conditions that the model need to adhere to in this case there are
three categories. One if the resource constraint which are
The total project cost need not exceed $ 20 million
The total land occupied by the golf resort is to be between 36 and 42
The second constraint is the type of the clubhouse that needs to be included in the resort.
It can either be a standard or an exclusive clubhouse.
Third we have the basic features that need to comprise an international golf resort these
are
at least:
One straight par 5,
One dogleg par 5,

Two straight par 4,
Two dogleg par 4,
One long par 3, and
One short par 3.
The course should have no more than 4 par 5’s.
The course should have no more than 14 par 4’s.
The course should have no more than 4 par 3’s.
The total par must be between 70 and 72.
The total number of holes must be exactly 18.
The total acreage must be between 36 and 42 hectares.
4. Mathematical expressions
For each of the models will have a mathematical expression of the objective function and
the constraints.
Standard clubhouse
This entails the idea of the managers to include a standard clubhouse at a cost of $ 3.5
million covering 2 hectares.
Model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6
S . t
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
y1 + y2+ y3+ y4 + y5 + y6=18
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72

5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≥ 70
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 2 x1 ≤ 42
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 2 x1 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +3500000 x1 ≥ 20000000
Model summary
Cunningham Golf Resort
Kind of golfing hole Straight par 5 Dogleg par 5 Straight par 4 Dogleg par 4 Long par 3 Short par 3
Par 5 5 8 40 3 9
Size (ha) 3 3.5 4 25 1 2.25
Enjoyment Index 2 1.5 3 20 1.75 6.75
Building cost $1,000,000 $1,500,000 $1,500,000 $9,000,000 $600,000 $1,950,000
Number of holes 1 1 2 10 1 3
>= >= >= >= >= >=
1 1 2 2 1 1
Clubhouse
Standard
Size 2
Enjoyment Index 0
Cost $3,500,000
Objective Function
Total Enjoyment Index 35
Constraints
Total cost $19,050,000 <= $20,000,000
Total Size 40.75 <= 42
Total Par 70 <= 72
Par 5 2 <= 4
Par 4 12 <= 14
Par 3 4 <= 4
Total Size 40.75 >= 36
Total Par 70 >= 70
Total holes 18 = 18
The exclusive clubhouse
This entails the shareholders request to construct an exclusive clubhouse at a cost of $ 6
million covering 4 hectares.
Model

Max ; 2 y1 +1.5 y2+ 1.5 y3 +2 y4 +1.75 y5 +2.25 y6 +4 x2
S . t
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
y1 + y2+ y3+ y4 + y5 + y6=18
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≥ 70
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 4 x2 ≤ 42
3 y1 +3.5 y2+2 y3 +2.5 y4 +1 y5 +0.75 y6+4 x2 ≥36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +6000000 x1 ≥ 20000000
Model summary

Kind of golfing hole Straighr par 5 Dogleg par 5 Straight par 4 Dogleg par 4 Long par 3 Short par 3
Par 4.999999975 5 40.0000002 8 9.000009 2.999991
Size (ha) 2.999999985 3.5 20.0000001 5 3.000003 0.7499978
Enjoyment Index 1.99999999 1.5 15.00000007 4 5.2500053 2.2499933
Building cost $1,000,000 $1,500,000 $7,500,000 $1,800,000 $1,800,002 $649,998
Number of holes 0.999999995 1 10.00000005 2 3.000003 0.999997
>= >= >= >= >= >=
1 1 2 2 1 1
Clubhouse
Exclusive
Size 4
Enjoyment Index 4
Cost $6,000,000
Objective Function
Total Enjoyment Index 33.99999856
Constraints
Total cost $20,250,000 <= $20,000,000
Total Size 39.25000083 <= 42
Total Par 70.00000017 <= 72
Par 5 1.999999995 <= 4
Par 4 12.00000005 <= 14
Par 3 4 <= 4
Total Size 39.25000083 >= 36
Total Par 70.00000017 >= 70
Total holes 18.00000004 = 18
Cunningham Golf Resort
Option 1
In this model the exclusive clubhouse model is to occupy 3.2 hectares
Model
Max ; 2 y1 +1.5 y2+ 1.5 y3 +2 y4 +1.75 y5 +2.25 y6 +4 x2
S . t
y1 ≥ 1
y2 ≥1
y3 ≥2

y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
y1 + y2+ y3+ y4 + y5 + y6=18
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≥ 70
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 3.2 x2 ≤ 42
3 y1 +3.5 y2+2 y3 +2.5 y4 +1 y5 +0.75 y6+3.2 x2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +6000000 x1 ≥ 20000000
Model Summary

Kind of golfing hole Straighr par 5 Dogleg par 5 Straight par 4 Dogleg par 4 Long par 3 Short par 3
Par 5 5 38.66666667 8 9 3
Size (ha) 3 3.5 19.33333333 5 3 0.75
Enjoyment Index 2 1.5 14.5 4 5.25 2.25
Building cost $1,000,000 $1,500,000 $7,250,000 $1,800,000 $1,800,000 $650,000
Number of holes 1 1 9.666666667 2 3 1
>= >= >= >= >= >=
1 1 2 2 1 1
Clubhouse
Exclusive
Size 3.2
Enjoyment Index 4
Cost $6,000,000
Objective Function
Total Enjoyment Index 33.5
Constraints
Total cost $20,000,000 <= $20,000,000
Total Size 37.78333333 <= 42
Total Par 68.66666667 <= 72
Par 5 2 <= 4
Par 4 11.66666667 <= 14
Par 3 4 <= 4
Total Size 37.78333333 >= 36
Total Par 68.66666667 >= 70
Total holes 17.66666667 = 18
Cunningham Golf Resort
Option 2
The construction cost of the exclusive clubhouse is modified to $ 5.1million
Model
Max ; 2 y1 +1.5 y2+ 1.5 y3 +2 y4 +1.75 y5 +2.25 y6 +4 x2
S . t
y1 ≥ 1
y2 ≥1
y3 ≥2

y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
y1 + y2+ y3+ y4 + y5 + y6=18
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≥ 70
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 3.2 x2 ≤ 42
3 y1 +3.5 y2+2 y3 +2.5 y4 +1 y5 +0.75 y6+3.2 x2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +5100000 x1 ≥ 20000000
Model summary

Kind of golfing hole Straighr par 5 Dogleg par 5 Straight par 4 Dogleg par 4 Long par 3 Short par 3
Par 10 5 28 16 3 9
Size (ha) 6 3.5 14 10 1 2.25
Enjoyment Index 4 1.5 10.5 8 1.75 6.75
Building cost $2,000,000 $1,500,000 $5,250,000 $3,600,000 $600,000 $1,950,000
Number of holes 2 1 7 4 1 3
>= >= >= >= >= >=
1 1 2 2 1 1
Clubhouse
Exclusive
Size 4
Enjoyment Index 4
Cost $5,100,000
Objective Function
Total Enjoyment Index 36.5
Constraints
Total cost $20,000,000 <= $20,000,000
Total Size 40.75 <= 42
Total Par 71 <= 72
Par 5 3 <= 4
Par 4 11 <= 14
Par 3 4 <= 4
Total Size 40.75 >= 36
Total Par 71 >= 70
Total holes 18 = 18
Cunningham Golf Resort
Option 3
In this option the exclusive clubhouse model is accepted but the constriction cost is
increased to $ 20.8 million.
Model
Max ; 2 y1 +1.5 y2+ 1.5 y3 +2 y4 +1.75 y5 +2.25 y6 +4 x2
S . t
y1 ≥ 1
y2 ≥1
y3 ≥2

y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
y1 + y2+ y3+ y4 + y5 + y6=18
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≤ 72
5 y1+ 5 y2 +4 y3 +4 y4 +3 y5+ 3 y6 ≥ 70
3 y1 +3.5 y2+ 2 y3 +2.5 y4 +1 y5 +0.75 y6+ 3.2 x2 ≤ 42
3 y1 +3.5 y2+2 y3 +2.5 y4 +1 y5 +0.75 y6+3.2 x2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +5100000 x1 ≥ 20800000
Model summary

Kind of golfing hole Straighr par 5 Dogleg par 5 Straight par 4 Dogleg par 4 Long par 3 Short par 3
Par 5 5 28 20 3 9
Size (ha) 3 3.5 14 12.5 1 2.25
Enjoyment Index 2 1.5 10.5 10 1.75 6.75
Building cost $1,000,000 $1,500,000 $5,250,000 $4,500,000 $600,000 $1,950,000
Number of holes 1 1 7 5 1 3
>= >= >= >= >= >=
1 1 2 2 1 1
Clubhouse
Exclusive
Size 4
Enjoyment Index 4
Cost $6,000,000
Objective Function
Total Enjoyment Index 36.5
Constraints
Total cost $20,800,000 <= $20,800,000
Total Size 40.25 <= 42
Total Par 70 <= 72
Par 5 2 <= 4
Par 4 12 <= 14
Par 3 4 <= 4
Total Size 40.25 >= 36
Total Par 70 >= 70
Total holes 18 = 18
Cunningham Golf Resort