Assume today's date to be February ${15}^{th},2024.$ K V Somanna owns a seventy acre coffee plantation in Coorg. He expects to harvest $1000$ Kilos of Herbaveda coffee beans in $45$ days, which he will then roast and package, ready to sell in an wholesale market. Today, the wholesale price of roasted Herbaveda coffee beans is $Rs\frac{250}{K}g.$ It is estimated that the wholesale price at any point will follow a lognormal distribution, with the mean differential monthly growth rate being $3\%,$ and a standard deviation of $8\%.$ K V Somanna decides to take a short position in the futures market for mangoes. The next settlement date is $60$ days from February ${15}^{th}.$ Assume that futures positions can be taken in multiples $10Kgs.$ The 'expected' futures price $E(F)=S**e^{rT},$ where $r$ is the risk free rate and $T$ is the time till expiration. Assume a risk$-$free rate of $6\%$ per annum. The actual futures price is$,F=E(F)+,$ where $$ is a random variable following a normal distribution with a mean of Rs $0$ and a standard deviation of $Rs\frac{5}{K}g.$ Further, it is truncated at the lower end at Rs $0.$ Today, on April ${15}^{th},$ the futures price is Rs $255\mathrm{.}0.$

a$.$ Supposing that K V Somanna is advised to take a short position somewhere between $0\mathrm{.}0$ Kilos and $1000$ Kilos. If K V Somanna wished to minimize the variance of the monetary value he will get on March ${31}^{st}2024,$ what must be his hedging strategy? Describe carefully how you will develop a Monte Carlo simulation model $($using @ Risk$)$ on the spreadsheet, which when executed will provide the answer you are looking for. In your answer, identify precisely all the random variables and how they are related to each other, if any. If K V Somanna wished to maximize the chance of exceeding Rs $2\mathrm{.}55$ lakhs, what should be his shorting position? $[$Use simulation with settings of Latin Hypercube, $5000$ iterations and a fixed starting seed of $7$ forall @Risk simulations$]$

points