It's rare to find an itinerary that is both the cheapest and takes the least time. You'll need to prioritise one over the other, or be prepared to compromise on both.

What is the most you're willing to pay to earn those 105 tier points? (Don't forget to factor in the cost of a hotel if necessary.) Are there any constraints on your time? (Can it be midweek? What's the maximum nights you can be away from home? etc.)