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Answer:
We require 2 buses and 18 vans for minimal cost
The minimal transportation costs $4560
Step-by-step explanation:
Let x represents the no. of buses and y represents the no. of vans
We are given that Each bus can transport 63 students, requires 2 chaperones, and costs $1200 to rent. Each van can transport 7 students, requires 1 chaperone, and costs $120 to rent.
We are also given that the officers must plan to accommodate at least 252 students.
So,
We are also given that the officers must plan to use at most 22 chaperones.
So,
Rent of 1 bus = $1200
Rent of 1 van = $120
So, Cost = 1200x+120y
Objective function : 1200x+120y
Plot the lines on graph
---- Blue region
----- Green region
So, The points of the feasible region are (4,0),(2,18) and (11,0)
At (4,0)
Transportation cost : 1200x+120y=1200(4)+120(0)=4800
At (2,18)
Transportation cost : 1200x+120y=1200(2)+120(18)=4560
At (11,0)
Transportation cost : 1200x+120y=1200(11)+120(0)=13200
So, The cost is minimum at (2,18)
So, We require 2 buses and 18 vans for minimal cost
Hence the minimal transportation costs $4560
