Meaning of "proportional" in Merriam Webster's interpretation of "scale" in business

Question

Merriam Webster has an article explaining the meaning of “scale” in business.

'Scale' is increasingly being used as shorthand for 'scale up' (“to grow or expand in a proportional and usually profitable way”)

https://www.merriam-webster.com/words-at-play/scale-the-business-meaning-origin

How can I interpret “proportional” here?

I checked this thread What does “scale” mean in “scale a media company / make media more scalable?

Or as a production process: if my plant costs $1B and produces X, a plant that produces 2X will not cost $2B, and the cost of my products will go down. Therefore I would rather build one giant refinery than many smaller ones (prices not... in scale).

I also checked this article. https://newdirectioncapital.com/difference-growth-scaling/

Scaling: When a company scales, it increases revenue, often at an exponential rate. But, the increase in resources required occurs at an incremental rate, if at all. A company that is scaling effectively is able to bring in $20 million worth of revenue for the same cost or nearly the same cost as it brought in $10 million.

If according to Merriam Webster, scale means “expand in a proportional way”, I don’t see how “scale” can mean increasing the revenue while keeping the same cost.

Answer 1

A scaled-up pilot plant would be expected to produce the same mix of products in similar proportions and have proportionate feedstocks and waste flows to the pilot plant. It may consist of multiple copies of the pilot plant running in parallel, or a bigger version of the pilot plant.

Scale does not necessarily imply any improvement in economies of scale. It just means developing and deploying the technology that physically allows a process to operate using a bigger plant. However, pilot plants are often built which are not economically viable (often due to high levels of instrumentation and lack of ready expertise, automation and control), but are close enough and worth it to get the bugs worked out, and as a trial run for regulatory compliance, and to test the product's market acceptability. So it is easy to understand that scaling up often has the built-in idea of transitioning from a pilot plant to an economically viable production system which uses tech developed from the pilot plant.

Scaling the tech and realizing economies of scale are two very different ideas best kept separate. Depending on the situation, they may be correlated well or not at all. If you are working in an industry that features extremely low marginal costs of production, the scaling up is just assumed to create profit. Where as in low value added industries, you can not make this assumption.