SOLUTION: Can you please help me with the constraints on this linear programming question? Trenton, Michigan, a small community, is trying to establish a public transportation system of l

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Question 175018: Can you please help me with the constraints on this linear programming question?
Trenton, Michigan, a small community, is trying to establish a public transportation system of large and small vans. It can spend no more than $100,000 for both sizes of vehicles and no more than $500 per month for maintenance. The community can purchase a small van for $10,000 and maintain it for $100 a month. The large vans cost $20,000 each and can be maintained for $75 per month. Each large van carries a maximum of 15 passengers, and each small van carries a maximum of 7 passengers.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the number of small vans and large vans purchased ,be S and L, respectively
:
10000S%2B20000L%3C=100000...eq 1 (for purchases)
:
100S%2B75L%3C=500...........eq 2(for maintanence)
:
divide equation 1 by 10000
:
s%2B2L%3C=10 revised eq 1
s%3C=5-%283%2F4%29Lrevised eq 2
:
take s's value in eq 2 and plug it into eq 1
:
5-%283%2F4%29L%2B2L%3C=10
:
multiply all terms by 4
:
20-3L%2B8L%3C=40
:
5L%3C=20
:
highlight%28L%3C=4%29
:
highlight%28s%3C=5-%283%2F4%29L%3C=5-%283%2F4%29%284%29%3C=2%29
:
so if we purchase 4 Large vans and 2 small vans we can carry
:
4(15)+2(7)=74 passengers