Why does the efficiency frontier manifest itself in a convex shape?

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The efficiency frontier shows all the different positions a firm can adopt with regard to adding value to the product and lowering cost assuming that its internal operations are configured efficiently to support a particular position.It has a convex shape because of diminishing returns.Diminishing returns imply that when a firm already has significant value built into its product offering,increasing value by a relatively small amount requires significant additional costs.The converse also holds,when a firm already has a low-cost structure,it has to give up a lot of value in its product offering to get additional cost reductions.

Why Does the Efficiency Frontier Manifest Itself in a Convex