











Rachael is planting two types of tree in the
garden: palm and beech.


Let x
be the number of palm trees and y be the number of beech trees to be planted.




She must grow at least 10 but no more than 80 palm trees.


She must grow at least 5 but no more than 40 beech trees.


She cannot grow more than 100 trees in total.


Each palm needs 20 litres of water and each beech
needs 60 litres of water each day.


There are 3000 litres of water available each day.




Rachel makes a profit of £2 on each palm tree and
£1 on each beech that she plants.


She wishes to maximise her profit. How many of each
type of tree should she plant?













P =


x +


y



























Enter two points for each constraint line to
generate a plot in the window below.



You should choose points which clearly show the
region formed by the constraints.

























Constraint 1

x

y







Point 1









Point2









Constraint 2

x

y







Point 1









Point2









Constraint 3

x

y







Point 1









Point 2









Constraint 4

x

y







Point 1









Point 2









Constraint 5

x

y







Point 1









Point 2









Constraint 6

x

y







Point 1









Point 2







































































Starting with the corner
point nearest the origin, (0, 0),
enter the corner points in clockwise order:


Give your answers rounded
to 2 decinmal places.







Calculate "P" based on your rounded answers.



















Feasible Region Corner Points

x

y

P





Corner Point 1








Corner Point 2








Corner Point 3








Corner Point 4








Corner Point 5








Corner Point 6








































The objective function is maximised at corner point
number:















