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Question 1
Question 1
Q1 Solution
Linear Programming
Q1)
A developer has a plot of land on which he can build either office units or houses.
Let
x
be the number of office units and let
y
be the number of houses to be built.
He decides to build:
at least 10 office units
(constraint 1),
at least 20 houses
(constraint 2).
Planning regulations prevent him from constructing more than 60 buildings in total (constraint 3).
Furthermore, he has the following restrictions on space:
Each office unit requires 400 m
2
and each house requires 200 m
2
of land. The entire plot of land is 16000 m
2
(constraint 4).
The builder makes a profit of £13,500 on each office unit and a profit of £9,500 on each house.
How many office units and house many houses should be built to maximise his potential profits?
Fill in the constraints below:
constraint 1:
x
+
y
constraint 2:
x
+
y
constraint 3:
x
+
y
constraint 4:
x
+
y
Fill in the Profit function below:
P =
x
+
y
Solve the linear programming problem and answer the following questions:
What is the number of office units to be built to maximise potential profit?
What is the number of houses to be built to maximise potential profit?
What is the maximum potential profit that can be made subject to the constraints?
Maximise the objective function subject to the following constraints (x,y
≥ 0 assumed)
:
Constraint 1
1
x
+
0
y
g
10
Constraint 2
0
x
+
1
y
g
20
Constraint 3
1
x
+
1
y
l
60
Constraint 4
400
x
+
200
y
l
16000
Constraint 5
x
+
y
Constraint 6
x
+
y
Objective Function
P=
13500
x
+
9500
y
The objective function is maximised at:
x =
y =
Here, the objective function has value:
P =
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Objective function (1 on, 0 off)
P=
x max
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