Calculating amount to sell in a forward contract

[Franjey]

Hi David,

Would you please help me with the following exercise? It says:

My field has 1000 hectares. The historical average production is 3 tons per hectare. The best possible scenario is to produce 5 tons per hectare. The worst, in drought, is 1 ton per hectare. The cost of production per ton is 1,500$.

How many tons do I sell forward to minimize the price risk of my production?

 

[Franjey]

@David Harper CFA FRM Have you seen any similar exercise like this in the past? I am just wondering if one should just go ahead and sell 3000 tons (average production), or if there is any trick behind.

 

[David Harper CFA FRM]

@Franjey I have not seen it before; this pattern is not something you'd seen on the FRM. It actually raises a few questions for me. I don't know, I'd guess 3,000 also but, either I'm missing something (very possible) or the question is naive: is asks us to minimize the "price of my production" yet seems to assume the cost per ton will be fixed at 1,500 and the quantity is variable.

What is the source, and do you have a given answer? happy to dissect further but i'd prefer to know it's a reliable source before spending time, thanks!