# What's the optimal way to size a limit order?

Say Bob wants to buy \$30 million worth of APPL stock at a price of \$130.

He decides to use a limit order.

But posting a $30 million limit order would drive the price up and prevent him from being filled. Obviously he must post only a fraction of this amount and then slowly top it up each time he gets filled. But what fraction? Should he post \$1 million? \$1000? or even \$10?