Question

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?

Answer 1

• 1 bus, 72 vans
• $6960 is the minimum cost

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.