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16 April, 14:01

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?

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Answers (1)
  1. 16 April, 15:01
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    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
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