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Linear Programming
Q2)
A hotel wants to create a children's play area. The space available for this is 80 m
2
.
The play area will contain
x
picnic tables and
y
play items (swings, slides, etc.).
Picnic tables take up 3 m of space and play items take up 2 m of space (constraint 1).
The number of picnic tables should be no less than double the number of play items (constraint 2).
The picnic tables cost £300 each and the play items cost £140 each.
Assume that the hotel wants to fill the whole space and minimise costs.
Fill in the constraints below:
constraint 1:
x
+
y
constraint 2:
x
+
y
Fill in the Cost function below:
C =
x
+
y
Solve the linear programming problem and answer the following questions:
What is the number of picnic tables to be built?
What is the number of play items to be built?
What is the minimum cost of building the play area given the constraints?
Maximise the objective function subject to the following constraints (x,y
≥ 0 assumed)
:
Constraint 1
x
+
y
l
Constraint 2
1
x
+
-2
y
g
0
Constraint 3
x
+
y
l
Constraint 4
x
+
y
l
Constraint 5
x
+
y
Constraint 6
x
+
y
Objective Function
P=
x
+
y
The objective function is minimised at:
x =
y =
Here, the objective function has value:
P =
Plotting Options
Show corner points ( 1 on, 0 off)
1
Objective function (1 on, 0 off)
1
P=
x max
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