l. Petroleum Industry Management A petroleum company has three plants. From a ba
ID: 3109586 • Letter: L
Question
l. Petroleum Industry Management A petroleum company has three plants. From a barrel of crude oil, factory #1 can produce 20 gallons of motor oil, 10 gallons of diesel oil and 5 gallons of gasoline. There is also waste in the form of paraffin, among other things. Similarly, factory#2 can produce 4 gallons, 14 gallons, and 5 gallons, respectively, while factory #3 can produce 4 gallons,5 gallons, and 12 gallons, respectively of motor, diesel, and gasoline. Factory #1 has 3 gallons of paraffin to dispose of per barrel of crude, factory #2 5 gallons, and factory #3 2 gallons. The current daily demand from distributors is 5000 gallons of motor oil, 8500 gallons of diesel oil and 10000 of gasoline. 1. Set up the system of equations which describes the above situation. 2. Next, decide how many barrels of crude oil each plant should get in order to meet the demand as a group. Remember that you can only provide each plant with an integer number of barrels. 3. Suppose the total demand for all products doubled. What would your solution now be? How does it compare to the original solution? In real life applications, constants are rarely ever exactly equal to their stated value; certain amounts of uncertainty are always present. This is part of the reason for the science of statistics. he above model, the daily productions for the plants would be averages over a period of time. 4. Explore what effect small changes in the parameters have on the output. To do this, pick any 3 coefficients, one at a time, and vary them one way and the other by 3%. For each case, note what effect this has on the solution, as a percentage change. Can you draw any overall conclusion?Explanation / Answer
3. If the demand of the all products is doubled, then we have to increase the supply of the products from each factory. The new current daily demand is given by as follows:
The demand of Motor oil = 2(5000)=10,000 gallons
The demand of diessel oil= 2(8500)= 17,000 gallons
The demand of Gasoline= 2(10,000)=20,000 gallons
From given specifications, we can change only the demand given above in answer (b). The new table for given values is formed as shown below:
From answer, we can see that the demand of motor oil, diesel oil and gasoline is double the previous demand 48.75, 331.25 and 675. It means that if we want to increase the production n times, then we have have to increase the product of every item in n times in each factory.
4). If we can increase the coefficient of f1 by 3% and other two variables f2 and f3 as constant, then new table for given values is formed as shown below:
Thus the total output per day by factory 1 decrease by 97.5 to 94.67.Thus decrease of output is (97.5-94.66)=2.83
Thus, % decrease in output is given by factory 1 is = (2.83/97.5)100=2.90%.The output of by factory 1 is decreased by approximately 3%. Here, we conclude that if we increase the value of cofficient by n% then its output is decreased by approximately n% and its vice-versa.
Factory 1 Factory 2 Factory 3 Total Demand Motor Oil 20 4 4 10,000 Diesel Oil 10 14 5 17,000 Gasoline 5 5 12 20,000 Barrels of oil(Exact) 97.5 662.5 1350 2110 Barrels of Oil(Approximate) 97 or 98 663 or 662 1350 2110Related Questions
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