rating of at least 10 and contain at most %1 sulfur. The crude oil blended to form gas 2 must have an average octane rating of at least 8 and contain at most %2 sulfur. The crude oil blended to form gas 3 must have an octane rating of at least 6 and contain at most %1 sulfur. The octane rating and the sulfur content of the three types of oil are given in the following table: Crude 1 Crude 2 Crude 3 Octane rating Sulfur content 12 0.5% 6 2% 8 3% It costs $4 to transform one barrel of oil into one barrel of gasoline, and Suncon's refinery can produce up to 14,000 barrels of gasoline daily. Sunco's customers require the following amounts of each gasoline: gas 1-3000 barrels per day; gas 2 - 2,000 barrels per day; gas 3- 1,000 barrels per day. The company considers it an obligation to meet these demands. Sunco also has the option of advertising to stimulate demand for its products. Each dollar spent daily in advertising a particular type of gas increases the daily demand for that type of gas by 10 barrels. For example, if Sunco decides to spend $20 daily in advertising gas 2, the daily demand for gas 2 will increase by 200 barrels. Formulate an LP model that will enable Sunco to maximize daily profits and solve it using Lingo. Interpret the result and the information in the slacks variables column.
rating of at least 10 and contain at most %1 sulfur. The crude oil blended to form gas 2 must have an average octane rating of at least 8 and contain at most %2 sulfur. The crude oil blended to form gas 3 must have an octane rating of at least 6 and contain at most %1 sulfur. The octane rating and the sulfur content of the three types of oil are given in the following table: Crude 1 Crude 2 Crude 3 Octane rating Sulfur content 12 0.5% 6 2% 8 3% It costs $4 to transform one barrel of oil into one barrel of gasoline, and Suncon's refinery can produce up to 14,000 barrels of gasoline daily. Sunco's customers require the following amounts of each gasoline: gas 1-3000 barrels per day; gas 2 - 2,000 barrels per day; gas 3- 1,000 barrels per day. The company considers it an obligation to meet these demands. Sunco also has the option of advertising to stimulate demand for its products. Each dollar spent daily in advertising a particular type of gas increases the daily demand for that type of gas by 10 barrels. For example, if Sunco decides to spend $20 daily in advertising gas 2, the daily demand for gas 2 will increase by 200 barrels. Formulate an LP model that will enable Sunco to maximize daily profits and solve it using Lingo. Interpret the result and the information in the slacks variables column.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:rating of at least 10 and contain at most %1 sulfur. The crude oil
blended to form gas 2 must have an average octane rating of at least
8 and contain at most %2 sulfur. The crude oil blended to form gas 3
must have an octane rating of at least 6 and contain at most %1 sulfur.
The octane rating and the sulfur content of the three types of oil are
given in the following table:
Crude 1
Crude 2
Crude 3
Octane rating Sulfur content
12
0.5%
6
2%
8
3%
It costs $4 to transform one barrel of oil into one barrel of gasoline, and
Suncon's refinery can produce up to 14,000 barrels of gasoline daily.
Sunco's customers require the following amounts of each gasoline: gas
1- 3000 barrels per day; gas 2 - 2,000 barrels per day; gas 3- 1,000
barrels per day. The company considers it an obligation to meet these
demands. Sunco also has the option of advertising to stimulate demand
for its products. Each dollar spent daily in advertising a particular type
of gas increases the daily demand for that type of gas by 10 barrels. For
example, if Sunco decides to spend $20 daily in advertising gas 2, the
daily demand for gas 2 will increase by 200 barrels.
Formulate an LP model that will enable Sunco to maximize daily profits
and solve it using Lingo. Interpret the result and the information in
the slacks variables column.
Transcribed Image Text:Exercise 3 Sunco Oil blending problem
Sunco Oil manufactures three types of gasoline (gas 1, gas 2, gas 3).
Each type is produced by blending three types of crude oil (crude 1,
crude 2, and crude 3). The sales price per barrel of gasoline and the
purchase price per barrel of crude oil are given in the following table:
Gas 1
Gas 2
Gas 3
Sales price per barrel
$70
$60
$50
Crude 1
Crude 2
Crude 3
Purchase price per barrel
$45
$35
$25
Sunco can purchase up to 5,000 barrels of each type of crude oil daily.
The three types of gasoline differ in their octane rating and sulfur con-
tent. The crude oil blended to form gas 1 must have an average octane
Expert Solution
Step 1
Suppose,
barrels of crude oil used daily to produce gas .
dollars spent on advertising daily.
So, barrels of crude 1 daily is:
.
and similarly barrels of gas 1 produced daily is:
.
Daily revenue from sale of gas is:
.
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