11 Answer the whole of this question on a sheet of graph paper.
A hired bus
is used to take learners and teachers on a
trip. The
number of leamers
and teachers must not be
more than 60. There
must be at least 35 people on the trip. There must be at least 6
teachers on the trip. The number of teachers on the trip should not
be more than 14. Let x be the number of leamers and y the number
of teachers.
(a) Write four inequalities which represent the information above[4]
(b) Using a scale of 2 cm to represent 10 units on both axes, draw
the x and y axes for 0 ≤ x ≤70 and 0 ≤ x ≤70 respectively
and shade the unwanted region to indicate clearly the region
where the solution of the inequalities lie.
[4]
(c) (1) If the group has 25 learners, what is the minimum number
of teachers that must accompany them?
[1]
(ii) if 8 teachers go on this trip, what is the maximum number
of learners that can be accommodated on the bus? [1]
(d) If T is the amount in Kwacha paid by the whole group, what is
the cost per learner if T = 30x + 50y?
[2]
​