Baldwin Company had $55,000$ shares of common stock outstanding on January $1,2024.$ On April $1,2024,$ the company issued $35,000$ shares of common stock. The company had outstanding fully vested incentive stock options for $25,000$ shares exercisable at $$10$ that had not been exercised by its executives. The average market price of common stock for the year was $$12.$ What number of shares of stock $($rounded$)$ should be used in computing diluted earnings per share?

Multiple Choice

$102,500$

$85,417$

$77,500$

$60,417$