SPM Addmath Linear Programming Q4

4. Setia Indah Secondary School will host a motivational camp. Participants of the camp are made up of x female pupils and y male pupils. The fee for a female pupil is RM100 and the fee for a male pupil is RM120. The number of pupils in the camp is based on the following constraints.I The maximum number of pupils attending the camp is 80 .

Il The ratio of the number of female pupils to male pupils is at least 1: 3.

III The total fees collected is not less than RM5 000 .(a) Write three linear inequalities that satisfy all the above constraints other than x \geqslant 0 and y \geqslant 0.

(b) Using a 2 \mathrm{~cm} scale for 10 pupils on the x -axis and the y -axis, construct and label the region R that satisfies all the above constraints.

(c) Using the graph obtained in (b), find

(i) the minimum number of male pupils if the ratio of the number of female to male pupils is 1: 3,

(ii) the maximum profit obtained if the school takes 25 \% of the total fees collected.