Students are planning a trip and are going to rent buses and

Students are planning a trip and are going to rent buses and vans. Each bus can transport 40 students, at a cost of $1200. Each van can transport 8 students at a cost of $100. Each bus must have 3 teachers as supervisors and each van needs 1 teacher as a supervisor. There are at least 400 students that are eligible for the trip and there are teachers that have volunteered as supervisors. How many vehicles of each type should be rented?

Solution

Hence feasible solutions are

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

At (10,0), Z= 12000

At (12,0), Z= 14400

at (7,15), Z = 9900

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

Bus Van Available No of students 40 8 400 Supervisors 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