Proteins can vary in size from approximately 40 to 34,000 amino acids. a. why is there a lower limit to the size of proteins? b. why is there an upper limit to the size of polypeptides?

There's a lower limit to the size of proteins for a functional domain size. If they wee lower than 40 they would not be able to maintain their fold. It is necessary for the number of residues to perform a particular biochemical function.

There's an upper limit to the size of polypeptides because the longer it is the longer the mRNA and the gene is. If it was larger it polypeptides would have debilitating mistakes hidden in the genes.

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Mitochondria produce atp, a high energy compound. atp is used for all sorts of enzyme-mediated reactions, such as making proteins/nucleotides/etc, certain compounds cross the cell membrane, muscles move, etc.  without this source of energy, a cell will die. it will not be able to repair itself, defend against pathogens, etc.