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) In addition to the existing constraints, suppose that GOC management wants to deliver at least 3 million barrels of refined products. What will be the new optimal solution with this constraint? b) Did the objective function value improve compared to the one in option (a)? Why (not)?
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) In addition to the existing constraints, suppose that GOC management wants to deliver at least 3 million barrels of refined products. What will be the new optimal solution with this constraint?
b) Did the objective function value improve compared to the one in option (a)? Why (not)?
![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%2F055e1352-1a5e-45fe-9027-fa850219ee4a%2Fy31v7np_processed.jpeg&w=3840&q=75)
![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%2F055e1352-1a5e-45fe-9027-fa850219ee4a%2F7tgpo06_processed.jpeg&w=3840&q=75)
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