The most prominent determinant for a "change in supply" is a change in the cost of an input that goes into the production of an output (final good).

This article uses the example of the input cream that is used in the production of the output butter in the UK.

Rising price of cream squeezes Dairy Crest's margins

“Cream prices, which determine input costs for the butter business, have increased substantially during the first quarter,” the company said.

“This will put pressure on margins in our butter business. We have reduced our promotional activity on Country Life, which is adversely impacting volumes but mitigating some of the margin pressure.” (underlining mine)

Here are some slides to walk you through a basic demand and supply model to illustrated how this impacts the market for butter as described in the article.