A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers. What is the minimum transportation cost? Make Vans equal"x"
Answers
Solution :-
Let school graduation class hire x vans and y buses .
given that,
- Each bus holds 40 students and 3 teachers and cost $1200 to rent .
- Each van holds 8 students and 1 teacher and costs $100 to rent .
- The school has at least 400 students wanting to go, but at most 36 teachers.
so, number of students (at least 400) :-
→ 8x + 40y ≥ 400
→ 8(x + 5y) ≥ 400
→ x + 5y ≥ 50
→ x ≥ (50 - 5y) ---------- Eqn.(1)
and, number of teachers (at most 36) :-
→ x + 3y ≤ 36
→ x ≤ (36 - 3y) --------- Eqn.(2)
Solving equality portion of both equations,
→ 50 - 5y = 36 - 3y
→ 50 - 36 = 5y - 3y
→ 14 = 2y
→ y = 7 .
putting value of y in Eqn.(1),
→ x = 50 - 5*7 = 50 - 35 = 15 .
then,
→ Minimum transportation cost = 15 vans + 7 buses = 15 * 100 + 7 * 1200 = 1500 + 8400 = $9900 (Ans.)
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