Linear Algebra Help for Norske-Norske Petrol Company

[msr_msr]

The Norske-Norske Petrol Company currently runs three refineries. The rst can produce 12 gallons of 87 octane gasoline, 7 gallons of 93 octane gasoline, 15 gallons of diesel, and 16 gallons of motor oil and 3 gallons of kerosene from a (55 gallon) drum of crude oil. The second can produce 13, 8, 14, and 22 gallons each of low- and high-test gasoline, diesel and oil, but no Kerosene. The third is an experimental plant which can produce 10 and 8 gallons of 97 and 93 octane gas respectively, but also produce 82 gallons of diesel and 22 gallons of motor oil by adding recycled oil at negligible cost. This plant also produces 9 gallons of kerosene in the process.

Please answer the following questions:
1. Create a matrix A for which A~x gives the total output (in thousands of gallons) of all three reneries, where ~x is the vector of supply, in thousands of barrels to each of the three factories.
2. Can the refineries meet the demand for 5620000 gallons of 83 octane gas, 3597000 ga. of 93 octane gas, 12531000 ga. of diesel, 9674000 ga. of oil, and 1002000 gallons of kerosene? If so, provide the number of (whole) barrels each renery must use.3. Can the rrefineries meet the demand for 22714866 gallons of 83 octane gas, 16342193 ga. of 93 octane gas, 12443727 ga. of diesel, 43255906 ga. of oil, and 14051280 gallons of kerosene? If so, provide the number of (whole) barrels each renery must use4. Can the refineries meet the demand for the supply vector h113210; 53030; 145270; 181470; 36300i? How can NNPC best supply the market? What assumptions must you make?

 

[HallsofIvy]

What have you done already? The first question, at least, should be straight forward.