a school graduation class wants to hire buses and vans for a trip to jasper national park. each bus hold 40 students and 3 teachers and costs $1200 to rent. each van holds 8 students and 1 teacher and cost $100 to rent. the school has at least 400 students wanting to go, but at most 36 teachers. what is the minimum transportation cost?
To determine the minimum cost of he transportation given the constraints and the costs of the transportation mode, we need to set up equations. We do as follows:
Let C be the total cost so that the total cost would have an expression:
C = 1200x + 100y where x is the number of buses and y is the number of vans to be rented.
We are given the total number of students, this would be equal to:
400 = 40x + 8y
Also, for the 36 teachers:
36 = 3x + y
We have three unknowns and three equation so we can solve the values of the unknowns. We do as follows:
36 = 3x + y y = 36 - 3x
400 = 40x + 8y 400 = 40x + 8(36 - 3x) x = 7
y = 36 - 3(7) y = 15
C = 1200x + 100y C = 1200(7) + 100(15) C = 9900 <------- minimum total cost
