Moli Labs Inc. is developing medical research on a certain anti-laziness pill. It is estimated that the lifetime value of the patent on this pill would be V = $1024 (in millions). The company can invest in many separate identical labs. Each lab costs $16 million to operate, and each has a probability = 0:5 of discovery. Find the profit-maximizing number of separate labs that the company should be investing in. Prove your result.