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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?

Respuesta :

Erythrosin17
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

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