how much oil is required when baking a cake [closed]

Oil is not required in a cake. There are different styles of cake, some have fats, others don't. For example, angel food cake and some European versions of bisquit dough don't use any oil. You can find ranges suggested for certain kinds of cake, for example Corriher has ranges for American style sponge cakes.

Not only is there no requirement for oil, but in cakes where oil is used, it doesn't help binding. If anything, it reduces binding. So your idea that their cakes are not binding because they are not using oil is wrong.

Now to the bakeries. They should 1) know what kind of cake they want, and 2) be working from a known good recipe for this kind of cake. They cannot start changing things around on the suggestion of a supplier.

If your product is not really useful with existing recipes, you can indeed try to give bakeries the recipes to use with it. But for creating a recipe from scratch, especially with a fickle product, and having it suitable for commercial use, you need a lot of expertise and a long process of refining and experimentation. As you seem to have very little basic understanding of cake chemistry (e.g. believing that oil binds cakes) you should probably hire a food technologist to either create the recipe or find suggestions for processing your eggs so they will bind in a standard recipe.