The school group may hire two types of camp sites: powered sites and unpowered sites.
Let
Inequality 1 and inequality 2 give some restrictions on
inequality 1
inequality 2
There are 48 students to accommodate in total.
A powered camp site can accommodate up to six students and an unpowered camp site can accommodate up to four students.
Inequality 3 gives the restrictions on
inequality 3
School groups must hire at least two unpowered camp sites for every powered camp site they hire.
- Write this restriction in terms of
and as inequality 4. (1 mark)
The graph below shows the three lines that represent the boundaries of inequalities 1, 3 and 4.
- On the graph above, show the points that satisfy inequalities 1, 2, 3 and 4. (1 mark)
- Determine the minimum number of camp sites that the school would need to hire. (1 mark)
- The cost of each powered camp site is $60 per day and the cost of each unpowered camp site is $30 per day.
- Find the minimum cost per day, in total, of accommodating 48 students. (1 mark)
School regulations require boys and girls to be accommodated separately.
The girls must all use one type of camp site and the boys must all use the other type of camp site.
- Determine the minimum cost per day, in total, of accommodating the 48 students if there is an equal number of boys and girls. (1 mark)