#4 A company runs three oil refineries, R1, R2, and R3. Each R, produces heating
ID: 334536 • Letter: #
Question
#4 A company runs three oil refineries, R1, R2, and R3. Each R, produces heating oil (HO), diesel oil (DO), and gasoline (G). Suppose that one barrel of crude oil produces the following number of gallons of heating oil, diesel oil, and gasoline in each refinery: R1 20 10 10 R2 R3 15 8 10 Demand 550 300 600 HO DO 3 10 The Demand for each product is given in thousands of barrels. A. Let x, be the number of barrels (in thousands) of crude oil processed by refinery R B. The company needs to shut down refinery R3 while continuing to meet the same (i-1,2,3), find the number of barrels needed to meet the demand demand. Make a recommendation to the company, support your recommendation and provide any additional information.Explanation / Answer
A). Ans:- Let X1, X2 and X3 barrels of creude oil processed by refinery R1, R2, and R3 respectively.
So, 20X1 + 5X2 + 15X3 = 550 - Eq 1
similarly, 10X1 + 3X2 + 8X3 = 300 - Eq 2
And, 10X1 +10X2+ 10X3 = 600 - Eq3
On subtracting Eq3 from Eq2 we get, 7X2 + 2X3 = 300
On Eq3*2 - Eq3*1, we get, 15X2 + 5X3 = 650,
On solving we get, X1 =10, X2 = 40, X3 = 10
Therefore 10 barrels, 40 barrels and 10 barrels should be processed by refinery R1,R2 and R3 refineries respectively.
B) Ans:- On shutting down refinery R3, one needs to increase the amount of barrels processed from refinery R1 and R2.
So, 20X1 + 5X2 = 550, 10X1 + 3X2 = 300 and 10X1 + 10 X2 = 600
So, X1 =17.15 and X2 =42.85
So, refinery R1 should process `17.15 barrel of crude oil and refinery R2 should process 42.85 barrel of crude oil.
Heating oil produced would be = 557.25 gallons
In this process all the demands would be met and additional 7.25 (557.25-550) gallons of heating oil would be produced, which should be consumed in other processes or sold.
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