Optimize Laravel App Performance

I need an experienced Linux administrator and PHP developer to tune the performance of my Laravel web application, APIs, and MySQL database on a VPS.

Current Issues:
- Server timeouts
- High CPU usage

Requirements:
- Optimize server configurations
- Implement caching mechanisms (preferably Redis or Memcached)
- Fine-tune MySQL queries and Laravel performance

Ideal Skills and Experience:
- Strong background in Linux administration
- Expertise in PHP, Laravel, and MySQL
- Experience with VPS hosting and performance tuning
- Knowledge of caching mechanisms like Redis or Memcached

Please provide a detailed plan and timeframe for completion.