Question

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 35 ​students, requires 2 ​chaperones, and costs ​$1400 to rent. Each van can transport 7 ​students, requires 1​ chaperone, and costs ​$90 to rent. Since there are 350 students in the senior class that may be eligible to go on the​ trip, the officers must plan to accommodate at least 350 students. Since only 26 parents have volunteered to serve as​ chaperones, the officers must plan to use at most 26 chaperones. How many vehicles of each type should the officers rnt in order to minimize the transportation​ costs? What are the minimal transportation​ costs?

Answer 1

	Bus	Van	Available
No of students	35	7	350
Chaperons	2	1	26
cost	1400	90

Let x be the no of buses and y the vans

Objective is to minimise total cost Z = 1400x + 90y

Then 35x+7y >=350 or 5x+y>=50

2x+y<=26

20 (8. 10) 50 40 30 -10 20 0(13,0) (10, 0) -30 10 20

Hence feasible solutions are

Z = 1400x + 90y

(10,0) (13,0) and (8,10)

Z for (10,0) = 14000

Z for (13,0) = 18200

Z for (8,10) = 12100

Hence minimal transportation cost is 12100 with 8 buses and 10 vans.