High School

Tim has two mountains to choose from: "Everest" and "Rocky."

- The day ticket costs $60 for Everest and $90 for Rocky, respectively.
- A one-way trip to Everest lasts 1.5 hours and costs $10 in gasoline expenses.
- A one-way trip to Rocky takes 30 minutes and costs $5 in gasoline expenses.

Tim would like to:
- Spend on average no more than 2.5 driving hours per trip.
- Ensure his total driving hours do not exceed 100 hours.

Question:
How many trips should Tim plan for each of these mountains so that the total cost is minimal if he wants to ski at least 20 days this season? What is the total cost of these trips?

Answer :

Based on the desired constraints, Tim should plan 20 trips to Everest and the remainder at Rocky hill. The total cost of these trips is $4250.

Tim's decision should be based on the total driving hours for each hill and the associated costs. For Everest, the total return trip time is 3 hours and costs $70.

For the Rocky, the total return trip takes 1 hour and costs $95. Thus, per day, Tim can take 2 trips to Everest (6 hours) or 2.5 trips to Rocky (2.5 hours), without exceeding the 2.5 hour driving limit.

If Tim's total driving hours must not exceed 100 hours, means he could make approximately 33 trips to Everest, or 40 trips to Rocky.

However, Rocky would cost more overall. Thus, Tim should plan 20 trips to Everest for a total cost of $1400, and the remainder of the season at Rocky, with a total cost of $2850, giving a combined total of $4250.

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