Final answer:
The spread between the average output (gasoline and heating oil) and input prices at the refinery on a barrel basis is $14.4 per barrel. This is calculated by subtracting the total input cost of $150 (for 3 barrels of WTI crude at $50/barrel) from the total output revenue of $193.2, which accounts for revenues from gasoline and heating oil sales.
Step-by-step explanation:
To calculate the spread between the average output (gasoline and heating oil) and input prices at the refinery on a barrel basis, we first need to compute the total output revenue and then subtract the input cost. For gasoline, the refinery sells 2 barrels at $1.5/gallon, and since one barrel holds 42 gallons, this results in $(2 × 42 × $1.5) of revenue. The revenue from heating oil is $(1 × 42 × $1.6) as there is 1 barrel at $1.6/gallon. Summing these revenues gives us the total output revenue. The input cost is straightforward: it is the contract price of WTI crude at $50/barrel for 3 barrels, hence $(3 × $50).
To find the spread, subtract the input cost from the total output revenue:
- Total revenue from gasoline: 2 × 42 × $1.5 = $126
- Total revenue from heating oil: 1 × 42 × $1.6 = $67.2
- Total output revenue: $126 + $67.2 = $193.2
- Total input cost: 3 × $50 = $150
- Spread: $193.2 - $150 = $43.2 per 3 barrels or $14.4 per barrel
The spread is $14.4 per barrel, representing the profit before any additional expenses for the refinery.