Suppose that call options on ExxonMobil stock with time to expiration 3 months and strike price $90 are selling at an implied volatility of 30%. ExxonMobil stock currently is $90 per share, and the risk-free rate is 4%. If you believe the true volatility of the stock is 32%, how can you trade on your belief without taking on exposure to the performance of ExxonMobil? How many shares of stock will you hold for each option contract purchased or sold?

When a company produces and sells x thousand units per week, its total weekly profit is p thousand dollars, where upper p equals startfraction 800 x over 100 plus x squared endfraction . the production level at t weeks from the present is x equals 4 plus 2 t. find the marginal profit, startfraction dp over dx endfraction and the time rate of change of profit, startfraction dp over dt endfraction . how fast (with respect of time) are profits changing when tequals8?