The common shares of Twitter, Inc. (TWTR) recently traded on the NYSE for $22.30 per share. You have employee stock options to purchase 1,000 TWTR shares for $21.7 per share. The options expire in three years. Assume that the annualized volatility of TWTR stock is 89.2 percent and that the interest rate is 2.9 percent. (Assume the options are European options that may only be exercised at the maturity date.)

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?