Self Test

Oil Refining, Energy Transportation, and Linear Programming

Circle whether the following statements are True or False. 

Click on True or False to test your knowledge of the chapter.

You can check your answers at http://www.mines.edu/Academic/courses/econbus/dahl/ebgn530/st14/st14.htm.

1.  True False  Crude oil is a chemical compound.  (Contributed by Benoit Gervais)

2.  True False  Catalytic cracking allows refineries to increase the amount of gasoline produced from a barrel of oil.  (Contributed by Benoit Gervais)

3.  True False  Lighter crude oil is always preferable.  (Contributed by Benoit Gervais)

4.  True False  Crude oil’s API gravity is its only important characteristics.  (Contributed by Benoit Gervais)

5.  True False  A distillation curve shows whether the whole barrel has been distilled or not.  (Contributed by Benoit Gervais)

6.  True False  The U.S. possesses the largest refineries in the world.  (Contributed by Benoit Gervais).

7.  True False Normal butane can be used to increase octane level beyond 100.  (Contributed by Benoit Gervais).

8.  True False  Blendco Inc. is a gasoline blender that makes regular (R) and premium gasoline (P).  Its recipe for each barrel of regular gasoline is 3/4 barrel of grade 1 blending stock (B1) and 3/5 gallon of grade 2 blending stock (B2).  Its recipe for each barrel of premium gasoline is 1/4 barrel of grade 1 blending stock and 2/5 barrel of grade 2 blending stock. The production functions for R is

            R = min[(4/3)B1, (5/3)B2)

(Contributed by Benoit Gervais)

9.  True False  Blendco Inc. is a gasoline blender that makes a net income of $1 for each barrel of regular gasoline (G) it produces and $1.50 for each barrel of premium gasoline (P) it produces. The firm currently has 120 barrels of grade 1 blending stock (B1) available and 50 barrels of grade 2 blending stock available (B2). As above its recipe for each barrel of regular gasoline is 3/4 barrel of grade 1 blending stock (B1) and 1/4 gallon of grade 2 blending stock (B2).  Its recipe for each barrel of premium gasoline is 2/5 barrel of grade 1 blending stock and 3/5 barrel of grade 2 blending stock.  If Blendco’s goal is to maximize profits, its problem can be formulated as the following linear program (LP):

     Maximize G + 1.5P

     Subject to:   0.75G + 0.25P < 150

                         0.4G + 0.6P < 50

                       B1, B2, G, P > 0

(Contributed by Benoit Gervais)

10. True False Take the above LP from Blendco

     Maximize G + 1.5P

     Subject to: 0.75R + 0.6P < 120

                       0.25G + 0.4P < 50

                       B1, B2, G, P > 0

The optimal profits are when the refiner produces 120 barrels of G and about 50 barrels of P.  (Contributed by Benoit Gervais)

11.  True False  Take the LP from Blendco

     Maximize G + 1.5P

     Subject to: 0.75R + 0.4P < 120

                       0.25G + 0.6P < 50

                       B1, B2, G, P > 0

At the optimum R = 120, and P = 50, the amounts of B1 and B2 blended to R and P are

            R         P

B1       90        30

B2       30        20

(Contributed by Benoit Gervais)

12.  True False  You want to find the cheapest way to transport gas from two underground storage depots (quantities stored are U1 and U2) to two local distribution companies (quantities demanded are D1 and D2). Let Xij denote the amount of shipment from source i to destination j and Tij be the cost of transport from depot i to company j.  The LP formulation of the problem to minimizing the total transportation cost is:

     Min C = T11X11 + T11X12 + T11X21 + T11X22

              Xij

First order conditions for this problem are

     Cx11 = 0,

     Cx12 = 0,

      Cx21 = 0,

      Cx22 = 0.

(Contributed by Benoit Gervais)

13.  True False  You want to find the cheapest way to transport gas from two underground storage depots (U1 and U2) to two local distribution companies (D1 and D2). The quantities supplied and demanded at each origin depot and each demand center together with the unit transportation cost are summarized in the following table.

The Unit Transportation Cost Matrix

                   D1    D2   Supply

            O1  20     30    200

            O2  10     40    100

   Demand  150   150   300

Let Xij denotes the amount of shipment from source i to destination j. The LP formulation of the problem minimizing the total transportation cost is:

     Min 20X11 + 30X12 + 10X21 + 40X22

     subject to:

     X11 + X12 = 200

     X21 + X22 = 100

     X11 + X21 = 150

     X12 + X22 = 150

     all Xij >=0

(Contributed by Benoit Gervais)

14. True False Pipelines are the cheapest way to transport natural gas.  (Contributed by Benoit Gervais)

15. True False  We have economies of scale when a greater quantity of goods or services produced by a same entity decreases the cost per unit.  If we have a production function Q = L2.  We expect that we have economies of scale.  (Contributed by Benoit Gervais)

16. True False  The US has the largest number of tankers registered.  (Contributed by Benoit Gervais)

17.  True False  Given that the distance between the Arabian Gulf and New York via the Suez canal is 8,318 statute miles and it takes around 15 hours to transit the canal, 468 hours is the minimum time necessary for a 320,000 dwt ship to transport oil between those two points assuming that the ship travels at 16 Knots.  (Contributed by Benoit Gervais)

18.  True False  The Suez canal is one of six important tanker bottlenecks at this time.  (Contributed by Benoit Gervais)

19.  True False The charter rate index Worldscale is based on a given tanker speed and size. Everything else being constant, the larger the value of the index, the smaller the tanker.  (Contributed by Benoit Gervais)

20.  True False  It is unlikely that a U.S. ship owner may desire to register its tanker in another country. Tankers are sometimes flown under flags of convenience.  This means they are registered in a country where tax rates, operating standards and environmental requirements are more lax.  Tankers flown under flags of convenience are more often involved in tanker accidents than other tankers.  (Contributed by Benoit Gervais)

21. True False  North America is the largest importer and exporter of petroleum.  (Contributed by Benoit Gervais)

22. True False  Coal transport is a big business. Seaborne transport of steam coal is about ¼ that of oil by tonnage and is one of the cheapest means of long distance coal transport.  (Contributed by Benoit Gervais)

23.  True False  Given 4000 barrels of straight run gasoline with a motor octane of 61.6, 6000 barrels of reformate with a motor octane of 84.4, 1000 barrels of light hydrocrackate with a motor octane of 73.7, 8000 barrels of cat cracked gasoline with a motor octane of 76.8, 3619.5 barrels of normal butane with a motor octane of 92, we would need 2243 barrels of alkylate with an octane of 95.9 to get a blended motor octane of 80.  (Contributed by Greta Goto)