Firm BestHockeySticks needs to buy rubber to manufacture their hockey pucks. Specifically, they need to buy 3 tons of rubber for next winter, January 2017 (T = 3/4). The future price of rubber is uncertain. Each ton of rubber can be used to manufacture 1000 pucks, each of which is sold for $2.50. The manufacturing has a fixed cost of $1200 per ton, plus the cost of rubber. Suppose that today rubber sells for $900/ton and interest rates are r = 10% continuously compounded, annual.

a. BestHockeySticks buys 2 Call options with strike K = 900 (the option allows to buy rubber for $1000/ton) at an upfront cost of $100 each. Write down a mathematical formula for the resulting net profit of BestHockeySticks at T = 1. Sketch the profit as function of future rubber price.

b. In addition to the above Call options, BestHockeySticks decides to enter into a Forward contract to purchase 1 ton of rubber at a fixed price of $970/ton. Plot the resulting net profit diagram of BestHockeySticks (rubber + forward + Calls). Label important points on the graph.