Saudi Arabia is a kingdom in the Middle East with an area of 865,000 square miles, occup...

Saudi Arabia is a kingdom in the Middle East with an area of 865,000 square miles, occupying about four-fifths of the Arabian Peninsula. With a population of about 10 million, this Muslim and Arab state is generally recognized as being formed in 1927 when Ibn Sa’ud united the country and was acknowledged as the sovereign independent ruler. Summer heat is intense in the interior, reaching 124°F, but it is dry and tolerable in contrast to coastal regions and some highlands, which have high humidity during the summer. Winters (December through February) are cool, with the coldest weather occurring at high altitudes and in the far north. A minimum temperature recorded at at-Turayf in 1950 was 10°F, and it was accompanied by several inches of snow and an inch of ice on ponds. Average winter temperatures are 74°F at Jidda and 58°F at Riyadh (the capital city), which has an annual precipitation of 2.5 to 3 inches.

After oil was discovered in Bahrain in 1932, many companies turned to Saudi Arabia and started exploring. Thus, in 1937, the American Arabian Oil Company, Inc. (AMARCO), was formed as a joint venture between Standard Oil Company of California (SOCAL) and the Government of Saudi Arabia to explore, produce, and market any petroleum found in the country. The year before, a geologist from SOCAL had discovered a small quantity of oil in the Eastern Province at Dammam Dome, on which the oil company town of Dhahran is now built. It was just beginning to be developed when another discovery was made—of what was to prove to be the largest oil field in the world. Called the Ghamar field, it would start Saudi Arabia on the road to becoming a highly developed country in just a generation. Located about 50 miles inland from the western shores of the Persian Gulf, the Ghamar field is a structural accumulation along 140 miles of a north–south anticline. The productive area covers approximately 900 square miles, and the vertical oil column is about 1,300 feet. It is generally considered to have recoverable reserves of about 75 billion barrels of oil. Total proven reserves in Saudi Arabia are estimated at more than 500 billion barrels, enough for more than a hundred years of production.

Since 1950, Saudi Arabia has experienced greater and more rapid changes than it had in the several preceding centuries. For example, during this time, as skilled nationals became available, more and more of the exploration, drilling, refining, and other production activities came under the control of the country. SOCAL was left primarily with the marketing and transportation functions outside the country.

During the 1960s, AMARCO increased its profitability substantially by hiring Dr. George Dantzig, then of the University of California, as a consultant. He supervised the development and implementation of LP models to optimize the production of different types of crude oils, their refining, and the marketing of some of their principal products. As a result of this effort, an operations research (OR) department was started in the company with the responsibility of continuing to review the firm’s operations to find other areas where costs might be decreased or profits increased by applications of OR.

Now attention is being focused on another aspect of one of the company’s small California refinery operations: the production of three types of aviation gasoline from the Saudi Arabian crude oil available. Recently, the marketing of petroleum products to the airline industry has become a rather substantial portion of AMARCO’s business. As shown in Figure 4.45, the three aviation gasolines, A, B, and C, are made by blending four feedstocks: Alkylate, Catalytic Cracked Gasoline, Straight Run Gasoline, and Isopentane.

In Table 4.14,TEL stands for tetraethyl lead, which is measured in units of milliliters per gallon (ml/gal). Thus, a TEL of 0.5 means there is 0.5 milliliter of tetraethyl lead per gallon of feedstock. Table 4.14 shows that TEL does influence the octane number but does not influence the Reid vapor pressure.

Each type of aviation gasoline has a maximum permissible Reid vapor pressure of 7. Aviation gasoline A has a TEL level of 0.5 ml/gal and has a minimum octane number of 80. The TEL level of aviation gasolines B and C is 4 ml/gal, but the former has a minimum octane number of 91, whereas the latter has a minimum of 100.

Assume that all feedstocks going into aviation gasoline A are leaded at a TEL level of 0.5 ml/gal and that those going into aviation gasolines B and C are leaded at a TEL level of 4 ml/gal. Table 4.15 gives the aviation gasoline data. A final condition is that marketing requires that the amount of aviation gas A produced be at least as great as the amount of aviation gas B.

Solve the linear programming model developed in Question 1.

(Reference Question 1)

AMARCO’s planners want to determine how the three grades of aviation gasoline should be blended from the available input streams so that the specifications are met and income is maximized. Develop an LP spreadsheet model of the company’s problem.