Farmer Fred knows that he will have to purchase $355$kg of Dynamic Shifter fertiliser when it comes time for him to sow his new season of crop, sometime in September or October. Exactly when he plants the crop will depend upon when temperatures get above $25$ degrees Celsius on a regular basis. Farmer Fred has had bad experiences with volatile Dynamic Shifter prices in previous years. His planned budget never seems to be executed due to prices being very different to his expectations, and in desperation he has sought the help of a friend, Hedger Harry. Hedger Harry has recommended that Fred use Dynamic Shifter futures to hedge his exposure to price movements in the fertiliser.

There are September and December futures contracts available. However, deeming the maturity of the September futures to be too soon, Fred decides to take out a long position on December delivered Dynamic Shifter futures at $$4\mathrm{.}22/$kg$.$

On September $23$ Fred decides that temperatures are high enough to sow the crop. He subsequently closes his position on December Dynamic Shifter futures, which are then trading at $$5\mathrm{.}53.$

a$)$If the spot price on September $23$ of Dynamic Shifter fertiliser is $$5\mathrm{.}76/$kg$,$ calculate the price per kg Farmer Fred ends up paying for the $355$kg of Dynamic Shifter he required. Ignore the effect of the time value of money. Give your answer in dollars and cents to the nearest cent.

Price$/$kg $=$ $

b$)$Farmer Fred is

by implementing the futures strategy