optimization: The officers of a high school senior class are planning to rent bu

Question

optimization: The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperons, and costs $1200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $100. Since there are 400 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 400 students. Since only 36 parents have volunteered to serve as chaperones, the officers must plan to use at most 36 chaperones. How many vehicle of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

Explanation / Answer

Hence feasible solutions are

(10,0) (12,0) and (7,15)

Z for (10,0) = 12000

Z for (12,0) = 14400

Z for (7,15) = 9900

Hence minimal transportation cost is 9900 with 7 buses and 15 vans.

Bus Van Available No of students 40 8 400 Chaperons 3 1 36 cost 1200 100 Let x be the no of buses and y the vans Objective is to minimise total cost Z = 1200x + 100y Then 40x+8y >=400 or 5x+y>=50 3x+y<=36

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