A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus
holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher
and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers.
What is the minimum transportation cost?

Let the school hire x buses and y vans.

A bus can hold 40 students and 3 teachers.
A van can hold 8 students and 1 teacher.

The number of students riding in buses and vans is at least 400, therefore
40x + 8y ≥ 400 (1)

The number of teachers riding in buses and vans is at most 36, therefore
3x + y ≤ 36 (2)

Write (1) and (2) as
y ≥ 50 - 5x (3)
y ≤ 36 - 3x (4)

The equality portion of the solution of (3) and (4) is
36 - 3x = 50 - 5x
2x = 14
x = 7 => y = 36 - 3*7 = 15

A graph of the inequalities indicates the acceptable solution in shaded color, as shown below.

The minimum cost of renting buses and vans is
7*$1200 + 15*$100 = $9900

Answer: The minimum cost is $9,900