If an economy produces its most wanted goods but uses outdated production methods, it is

--the answer is "it is not achieving productive efficiency. But doesn't productive efficiency mean using the "least cost method of production"? So if you use outdated production method, aren't you utilizing the least cost method ?

You are correct that productive efficiency refers to producing output at the lowest possible cost, which is achieved by using the most efficient production methods available. While outdated production methods might be less costly in terms of immediate expenses, they are not necessarily the least cost method in terms of long-term efficiency.

Outdated production methods often involve obsolete technologies, inefficient processes, or a lack of innovation. This can result in higher input costs, lower productivity, and lower quality output compared to more modern and efficient methods.

To answer your question, if an economy produces its most wanted goods but continues to use outdated production methods, it is not achieving productive efficiency. Achieving productive efficiency would require the economy to adopt more efficient and cost-effective production methods that can maximize output while minimizing input costs.