A refinery blends three petroleum components into three grades of gasoline –regular, premium, and diesel. The maximum quantities available of each component and the cost per barrel are as follows: Component Cost/Barrel Maximum Barrels Available/Day A 9 6,000 B 7 3,000 C 10 4,500 To ensure that each gasoline grade retains certain essential characteristics, the refinery has put limits on the percentages of the components in each blend. The limits, as well as the selling prices for the various grades, are as follows:
Grade Selling Price/Barrel Component Specifications
R (regular) 18 Not less than 30% of A
Not more than 30% of B
Not less than 30% of C
P (premium) 25 Not less than 60% of C
A (diesel) 15 Not more than 50% of B
less than 10% of A
The refinery wants to produce at least 5,000 barrels of each grade of gasoline. The management wishes to determine the optimal mix of the three components that will maximize profit.
a. Define the decision variables.
b. Build an objective function.
c. Build all the constraints.

Answer and explanation:

Introduction

First of all, when talking about the Islamic Empire, it's necessary to go back to the birth of Islam in the year 610 CE, geographically locating ourselves in Mecca, where Saudi Arabia is located nowadays. The Islam was born by the hand of Muhammed, after his many territorial conquests.

Subsequent to his death, the so-called golden age of Islam began, and shortly after its expansion took place.

(Document A, provided by the website "Ducksters" on its history category. https://www.ducksters.com/history/islam/ )

Expansion  

The expanse of the Islamic Empire happened during the middle age and turned into one of the largest empires to ever exist, rapidly conqueering both Palestine and Mesopotamia territory. By the year 640, Alexandria was a major target and Islamic army took about two years in order to win this territory. Finally, after these lands had been successfully occupied, it was the turn of Northern Africa.

(Document A, provided by the website "Ducksters" on its history category. https://www.ducksters.com/history/islam/

Document B, provided by the website "Khanacademy". https://www.khanacademy.org/humanities/world-history/medieval-times/spread-of-islam/a/the-rise-of-islamic-empires-and-states)