Question 755186: each bus holds 40 students and 3 teacher and costs $1200 to rent. Each van holds 8 student and 1 teacher and cost $100 to rent. The school has at least 400 student wanting to go, but at most 36 teachers. What is the minimum transportation cost? Make V ans equal "x"
Answer by josgarithmetic(39800)   (Show Source):
You can put this solution on YOUR website! Trying to fit this with variables and equations does not give me anything, so trying to think practical-like, you would want to use as many vans as possible until you run out of either uncarried teachers or students.
Along that thinking, you fill 36 vans carrying 36 teachers and 288 students. This leaves no uncarried teachers but 112 uncarried students still needing transportation.
You want to unpack vans one by one until you can make available at least 1 teacher for 40 or less students.
Unpack 1 van. Get 1 teacher and 8+112=120 students. You need more teachers.
Unpack 2 vans. Get 2 teachers and 8+8+112=128 students. You need more teachers.
Unpack 3 vans. Get 3 teachers and 8+8+8+112=136 students.
Unpacking 3 vans allows you 3 busses each with 40 students & 1 teacher, and 1 bus still needing a teacher.
Unpack 4 vans. Get 4 teachers and 32+112=144 students.
Now, this will be 3 busses with 40 students each and 1 teacher each PLUS 1 more buss with 24 students and 1 teacher.
So how many vans now? 36-4=32 vans.
How many buses now? 4 busses.
COST= 32*100+4*1200
COST =8000 dollars.
Note that hopefully my using only 1 teacher per 40 or less students on a bus is permitted. Your description ALLOWS for 3 teacher per bus, but my objective was to use as many vans as possible, and believing that 1 teacher for a group of 40 students would be enough teachers. I did not interpret the 3 teacher per bus as a requirement.
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