$2.$ On December $11,2017,$ the WTI spot price was $$58$ per barrel. The WTI futures price on

December $11,2017,$ for delivery in December $2020,$ was $$52$ per barrel.

$($a$)$ What is the name for the futures price structure on December $11,2017?$

$($b$)$ Suppose you are an energy consultant providing advice to a large oil trading firm. The

firm owns $10$ million barrels of oil in storage. Storage costs are $$1$ per barrel per

year and the firm has sufficient storage capacity to increase the quantity of oil in storage

to a maximum of $20$ million barrels. Annual interest rates are $5$ percent.

Suggest an optimal trading strategy for the firm that will maximize profits. You may

use any combination of spot market and futures market trades. The only constraint

is that the firm needs to have $10$ million barrels of oil available in three years time

$($December $2020)$