Aschool 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

The minimum cost is $9,900