Question

7.11. Consider production ratios of 2:1:1, 3:2:1, and 5:3:2 for oil, gasoline, and heating oil. Assume that other costs are the same per gallon of processed oil.

a. Which ratio maximizes the per-gallon profit if oil costs $80/barrel, gasoline is $2/gallon, and heating oil is $1.80/gallon?

b. Suppose gasoline costs $1.80/gallon and heating oil $2.10/gallon. Which ratio maximizes profit?

c. Which spread would you expect to be most profitable during the summer? Which during the winter?

Answer 1

a. Cost of Oil (per gallon) $80

Cost of Gasoline (per gallon) $2

Cost of Heating Oil (per gallon) $1.80

As per the Production Ratios;

Following Ratios	Oil	Gasoline	Heating Oil	Total Costing ($)
(2:1:1)	$80*2/4 = $40	$2*1/4 = $0.5	$1.80*1/4 = $0.45	$40 + $0.5 + $0.45 = $40.95
(3:2:1)	$80*3/6 = $40	$2*2/6 = $0.67	$1.80*1/6 = $0.3	$40 + $0.67 + $0.3 = $40.97
(5:3:2)	$80*5/10 = $40	$2*3/10 = $0.6	$1.8*2/10 = $0.36	$40 + $0.6 + $0.36 = $40.96

So the ratio which can maximize the profit would be (2:1:1) as under it the cost would be minimized to $40.95

b. Now if the Gasoline costs around $1.8 and heating oil cost around $2.10 per gallon then as per the production ratios costing would be;

Cost of Oil (per gallon) $80

Cost of Gasoline (per gallon) $1.80

Cost of Heating Oil (per gallon) $2.10

Following Ratios	Oil	Gasoline	Heating Oil	Total Costing ($)
(2:1:1)	$80*2/4 = $40	$1.80*1/4 = $0.45	$2.10*1/4 = $0.50	$40 + $0.525 + $0.45 = $40.975
(3:2:1)	$80*3/6 = $40	$1.80*2/6 = $0.60	$2.10*1/6 = $0.35	$40 + $0.60+ $0.35 = $40.95
(5:3:2)	$80*5/10 = $40	$1.80*3/10 = $0.54	$2.10*2/10 = $0.42	$40 + $0.54 + $0.42 = $40.96

So the ratio which can maximize the profit would be (3:2:1) as under it the cost would be minimized to $40.95

c. During summer gasoline produced is more expensive than in winters so during the summers company will go for the Production ratio of (2:1:1) as it would maximize the profit while in winters with lower prices of gasoline company will go for the production ratio of (3:2:1).