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
D) x21 + x22 = 8000

Answer 1

option c) x₁₁ + x₁₂ = 8000

Explanation:

Given:

xij = gallons of component i used in gasoline j

gallons of component 1 available = 8,000

demand gasoline types 1 = 11,000

demand gasoline types 2 = 14,000

Here, we have only component 1 available i.e i = 1 only

( therefore, all the options containing i = 2 gets eliminated )

thus,

component 1 will fulfill the demand of gasoline types 1 and 2 i.e j = 1 and 2

hence,

the equation satisfying the above conditions comes out as:

x₁₁ + x₁₂ = 8000

that means gallons of component 1 used in gasoline 1 and 2 and the total equals to the gallons of component 1 available i.e 8000