Large Language Models (LLMs) excel in diverse applications including generation of code snippets, but often struggle with generating code for complex Machine Learning (ML) tasks. Although existing LLM single-agent based systems give varying performance depending on the task complexity, they purely rely on larger and expensive models such as GPT-4. Our investigation reveals that no-cost and low-cost models such as Gemini-Pro, Mixtral and CodeLlama perform far worse than GPT-4 in a single-agent setting. With the motivation of developing a cost-efficient LLM based solution for solving ML tasks, we propose an LLM Multi-Agent based system which leverages combination of experts using profiling, efficient retrieval of past observations, LLM cascades, and ask-the-expert calls. Through empirical analysis on ML engineering tasks in the MLAgentBench benchmark, we demonstrate the effectiveness of our system, using no-cost models, namely Gemini as the base LLM, paired with GPT-4 in cascade and expert to serve occasional ask-the-expert calls for planning. With 94.2\% reduction in the cost (from \$0.931 per run cost averaged over all tasks for GPT-4 single agent system to \$0.054), our system is able to yield better average success rate of 32.95\% as compared to GPT-4 single-agent system yielding 22.72\% success rate averaged over all the tasks of MLAgentBench.