Question

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

a) x21 + x22 = 8000
b) x12 + x22 = 8000
c) x11 + x12 = 8000

Answer 1

c) x11 + x12 = 8000

Explanation:

Xij = Gallons of the ith component used in the jth Gasoline type

This invariably tells us what component is in which gasoline type.

The gasoline types are:

Gasoline 1 = 11,000 gallons

Gasoline 2 = 14,000 gallons

Assuming two(2) components types:

Component 1

Component 2

The possible combinations Xij are :

Gasoline 1 Gasoline 2

Component 1 X11 X12

Component 2 X21 X22

From the above , it is clear that the supply constraint for component 1 across the gasoline types is given by X11 & X12

Mathematically, since there are 8,000 gallons of Component 1, the supply constraint is given by:

X11 + X12 = 8000