Normally, an affiliate is a company in which another company or entity has a minority interest. (This is different from a subsidiary, in which a company has more than 50% control.) Under those circumstances, I don't see how the company can bind its affiliate in a contract.
But Company B signed a contract with Company C, binding itself to sell all of its widget production, and that of its "affiliate" A, at a fixed price to C. In the relevant contract, Company B defined "affiliate" (perhaps improperly) as a company it controls. In point of fact, the "control" percentage was 80%.
Can Company B so bind A with 80% control? How about 40% ownership?