Problem 1. IV Burritos needs to buy corn to manufacture their burritos. Specifically, they need to buy 2.5 tons of corn for the coming spring, May 2024(T=1/2). The future price of corn is uncertain. From 2.5 tons of corn they can make 15,000 burritos, each sold for $14. The cost (labor, rent, other ingredients) of a burrito is $12, plus the cost of the corn. Unfortunately the price of corn is very volatile and can easily go up/down 50% in a few months. Suppose that today corn sells for S0=$5200/ ton and interest rates are r=3.6% continuously compounded, annualized. a. As a hedge, IV Burritos also buys 1 Call option with strike K=5500 (the option gives the right to buy 1 ton of corn for $5500 at T ) at an upfront premium of $2000. Write down a mathematical formula for the resulting net profit (profit from selling burritos and profit of call) of IV Burritos at T=1/2. Plot the resulting net profit diagram of IV Burritos (15,000 burritos +1 Call Option) in the range ST[4500,6500], where ST is the corn price on 5/1/2024. Label important points on the graph. b. In addition to the above Call options, IV Burritos decides to enter into a Forward contract to purchase 1 ton of corn at a fixed price of $6000/ ton in May 2024. Plot the new resulting net profit diagram of IV Burritos (burritos + forward + Call) in the range ST[4500,6500]. Label important points on the graph