GulfOil Company (GOC) can buy two types of crude oil: light oil at $49/barrel and heavy oil $45/barrel. When a barrel of oil is refined it yields gasoline, jet fuel, and kerosene in the quantities, shown in the table (in terms of barrel of output per barrel of input). GOC has promised to deliver at least 800,000 barrels of gasoline, 900,000 barrels of jet fuel and 850,000 barrels of kerosene. a) Write a Linear Programming (LP) formulation that keeps promises and minimizes total oil purchase cost. Assume oil can be purchased in fractions. b) Find and state the optimal solution. c) Compare additional cost of delivering one more barrel of Jet Fuel vs that of Kerosene?
GulfOil Company (GOC) can buy two types of crude oil: light oil at $49/barrel and heavy oil $45/barrel. When a barrel of oil is refined it yields gasoline, jet fuel, and kerosene in the quantities, shown in the table (in terms of barrel of output per barrel of input). GOC has promised to deliver at least 800,000 barrels of gasoline, 900,000 barrels of jet fuel and 850,000 barrels of kerosene.
a) Write a Linear Programming (LP) formulation that keeps promises and minimizes total oil purchase cost. Assume oil can be purchased in fractions.
b) Find and state the optimal solution.
c) Compare additional cost of delivering one more barrel of Jet Fuel vs that of Kerosene?
![Gasoline Jet Fuel Kerosene
Light oil
0.43
0.20
0.29
Heavy oil 0.32
0.38
0.21](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F091e15d2-7260-4545-9276-1090fe0c8451%2F94cead4c-d53c-4b22-9899-ffddc9fdc79b%2Fdimyjwj_processed.jpeg&w=3840&q=75)
![1.Brewery
2.0il Refinery
••.
A
D
G
J
K
L
1
Oil Refinery Problem
Decision Variables:
Barrels
Gasoline
Kerosene
0.29
0.21
|Jet Fuel
Price
Light oil
Heavy oil
$ 49
$ 45
X1: # of barrels of light oil to purchase
X2: # of barrels of heavy oil to purchase
4.
0.43
0.20
0.32
0.38
Constraints:
Gasoline
Jet Fuel
Kerosene
Produced
9
>=
>=
>=
10
Promised
800,000
900,000
850,000
11
12 Objective Function:
Total Purchase Cost $
13
14
15
Total Production:
16
17
18
19
20
21
22
23
24
25
26
27](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F091e15d2-7260-4545-9276-1090fe0c8451%2F94cead4c-d53c-4b22-9899-ffddc9fdc79b%2Fcxyxqrw_processed.jpeg&w=3840&q=75)
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