The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 6363 students, requires 88 chaperones, and costs $1 comma 2001,200 to rent. Each van can transport 77 students, requires 1 chaperone, and costs $8080 to rent. Since there are 567567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567567 students. Since only 8080 parents have volunteered to serve as chaperones, the officers must plan to use at most 8080 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

Question

Mathematics

Brooklyn Buck

18 January, 14:05

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 6363 students, requires 88 chaperones, and costs $1 comma 2001,200 to rent. Each van can transport 77 students, requires 1 chaperone, and costs $8080 to rent. Since there are 567567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567567 students. Since only 8080 parents have volunteered to serve as chaperones, the officers must plan to use at most 8080 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

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Answers (1)

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Emerson Molina · Answer 1

1 bus, 72 vans $6960 is the minimum cost

Step-by-step explanation:

A bus costs over $19 per student; a van costs less than $12 per student. The required number of students could be transported by 81 vans, but that requires 81 chaperones.

Since there are only 80, and a bus requires fewer chaperones per student, we can reduce the number of required chaperones to an acceptable level by employing one bus. 1 bus replaces 9 vans, and requires 1 less chaperone than 9 vans.

The minimum cost is 1 bus and 72 vans. That cost is $1200 + 72*$80 = $6960.