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 ​$ 1,200 to rent. Each van can transport 77 ​students, requires 1​ chaperone, and costs ​$80 to rent. Since there are 567 students in the senior class that may be eligible to go on the​ trip, the officers must plan to accommodate at least 567 students. Since only 80 parents have volunteered to serve as​ chaperones, the officers must plan to use at most 80 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation​ costs? What are the minimal transportation​ costs?

Accepted Solution

Answer:Rent 8 vans, total cost 640 dollarsStep-by-step explanation:Since a van can accomodate 77 students and 1 chaperone. To accomodate 567 students vans needed are567/77 = 7.3Rounding it off to 8 vansIf the officer places 71 student and 8 chaperones in a van. He can accomodate 65 chaperones and 567 students. 71x8 = 568But we have only 567 students so in 1 van there will be 70 students and 9 chaperons. For chaperons(7x8) + (1x9) = 65Total cost for transportation will be 8 x 80 = 640 dollars