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Linear Programming
Q3)
A new cinema is being built which will contain standard seating and luxury seating.
Let
x
be the number of standard seats and let
y
be the number of luxury seats.
There must be no fewer than 600 seats (constraint 1) and…
…there must be no more than 1000 seats in total (constraint 2).
Each standard seat requires 0.75 m
2
and each luxury seat requires 2 m
2.
The area available for the theatre seating is 800 m
2
, (constraint 3).
There must be no less than 5 times as many standard seats as there are luxury seats (constraint 4).
The cinema will charge movie goers £9 for a standard seat and £12 for a luxury seat.
Fill in the constraints below:
constraint 1:
x
+
y
constraint 2:
x
+
y
constraint 3:
x
+
y
constraint 4:
x
+
y
Fill in the Revenue function below:
R =
x
+
y
Solve the linear programming problem and answer the following questions:
What is the number of standard seats to be built to maximise potential profit?
What is the number of luxury seats to be built to maximise potential profit?
What is the maximum potential revenue that can be made on a film show subject to the constraints?
Maximise the objective function subject to the following constraints (x,y
≥ 0 assumed)
:
Constraint 1
1
x
+
1
y
g
Constraint 2
1
x
+
1
y
l
Constraint 3
x
+
y
l
Constraint 4
1
x
+
y
g
0
Constraint 5
x
+
y
Constraint 6
x
+
y
Objective Function
P=
x
+
y
The objective function is maximised 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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