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Linear Programming
Q4)
Leone is designing her new garden.
She wants to have at least 1000 m
2
, split between lawn and flower beds.
Let
x
be the area of lawn and let
y
be the area of flower bed in her garden design.
lawn costs 80 pence per m
2
and flower beds cost 40 pence per m
2
and her budget is £500.
Leone prefers flower beds to lawn and wants the area of flower beds to be at least twice the lawn area.
She also wants at least 200 m
2
of lawn area.
Maintenance costs each year are 15 pence per square metre of lawn and 25 pence per square metre of flower bed.
Leone wants the maintenance costs to be as low as possible.
Fill in the constraints below:
constraint 1
x
+
y
constraint 2 in £
x
+
y
constraint 3:
x
+
y
constraint 4:
x
+
y
Fill in the Mantenance Cost function below:
C =
x
+
y
Solve the linear programming problem and answer the following questions:
What area of lawn should be laid to minimise maintenance costs?
What area of flower bed should be planted to minimise maintenance costs?
What is the minimum annual maintenance cost for Leone's garden?
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