Case Study: Linear Programming for Cunningham Gudgal Golf Resort Plan

This assignment provides a comprehensive linear programming action plan for the Cunningham Gudgal Golf Resort development project. It defines decision variables related to the number of different types of golf holes (straight par 5, dogleg par 5, straight par 4, dogleg par 4, long par 3, and short par 3) and formulates an objective function to maximize the total enjoyment index. The model incorporates various constraints, including minimum and maximum limits on the number of each type of hole, total size limitations, budget constraints, total par constraints, and the total number of holes. The assignment presents several mathematical models including a standard model and exclusive clubhouse models with different options, outlining the constraints and objective functions for each scenario. An alternate model is also provided, offering a different approach to the optimization problem. The goal is to determine the optimal mix of golf holes and clubhouse options to maximize enjoyment while adhering to all project constraints. Desklib provides students access to a wealth of similar solved assignments and past papers.

Part 1: Action plan
1. Decision variables
The decision variable of the number of golf holes that are to be constructed for each type
of golf hole. If we let the number of the golf holes be represented by y.
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
2. Objective function
The objective of the linear programming is to maximise the total enjoyment index of the
project.
3. Constraints
These are the conditions that the linear program have to adhere to they include;
Straight par 5>= 1
Dogleg par 5 >= 1
Straight par 4>= 2
Dogleg par 4 >= 2
Long par 3 >= 1
Short par 3 >= 1
Par 5 <= 4
Par 4 <= 14
Par 3 <= 4
Total Size <= 42
Total Size >= 36
Total Cost <= $20,000,000
Total Par <= 72
Total Par >= 70
Number of holes= 18

Another constraint of the project is the clubhouse to be constructed by the firm. This is
represented by t. where;
t1=standard clubhouse
t2=Exclusive clubhouse
4. Mathematical representation of the constraints and the objective function
Standard model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6
s . t
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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+2t1 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 2t1 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+ 650000 y6 +3500000 t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t

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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 6000000t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 1
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+3t2
s . t
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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 4500000 t1 ≤20000000
y1 ≥ 1
y2 ≥1

y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 2
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t
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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 +5200000 t1 ≤ 20000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Exclusive model option 3

Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+4t2
s . t
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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 4 t2 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 6000000t1 ≤ 22000000
y1 ≥ 1
y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4
Alternate model
Max ; 2 y1 +1.5 y2+1.5 y3 +2 y4 +1.75 y5 +2.25 y6+2 t1
s . t
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
y1 + y2+ y3+ y4 + y5 + y6=18
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+ 3t1 ≤ 42
3 y1+ 3.5 y2+2 y3 +2.5 y4 +1 y5+0.75 y6+3t1 ≥ 36
1000000 y1+1500000 y2 +750000 y3+ 900000 y4 +600000 y5+650000 y6 + 4000000 t1 ≤20000000
y1 ≥ 1

y2 ≥1
y3 ≥2
y4 ≥ 2
y5 ≥1
y6 ≥1
y1 + y2 ≤ 4
y3 + y4 ≤ 14
y5 + y6 ≤ 4