Answer:
The model is:
z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃ to maximize
Subject to:
First center X₁₁ + X₂₁ + X₃₁ ≤ 550
Second center X₁₂ + X₂₂ + X₃₂ ≤ 750
Third center X₁₃ + X₂₃ + X₃₃ ≤ 275
22* X₁₁ + 16* X₂₁ + 9*X₃₁ ≤ 11000
22* X₁₂ + 16* X₂₂ + 9*X₃₂ ≤ 2700
22*X₁₃ + 16* X₂₃ + 9*X₃₃ ≤ 3400
X₁₁ + X₁₂ + X₁₃ ≤ 710
X₂₁ + X₂₂ + X₂₃ ≤ 900
X₃₁ + X₃₂ + X₃₃ ≤ 350
2700*(X₁₁ + X ₂₁ + X₃₁) - 11000*(X₁₂ + X₂₂ + X₃₂) = 0
3400*(X₁₁ + X ₂₁ + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0
Xij >= 0
Step-by-step explanation:
Let´s call Xij product size i produced in center j
According to this, we get the following set of variable
X₁₁ product size huge produced in center 1
X₁₂ product size huge produced in center 2
X₁₃ product size huge produced in center 3
X₂₁ product size average produced in center 1
X₂₂ product size average produced in center 2
X₂₃ product size average produced in center 3
X₃₁ product size-tiny produced in center 1
X₃₂ product size-tiny produced in center 2
X₃₃ product size-tiny produced in center 3
Then Objective function is
z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃
Constrains
Center capacity
1.- First center X₁₁ + X₂₁ + X₃₁ ≤ 550
2.- Second center X₁₂ + X₂₂ + X₃₂ ≤ 750
3.- Third center X₁₃ + X₂₃ + X₃₃ ≤ 275
Water available
1.- 22* X₁₁ + 16* X₂₁ + 9*X₃₁ ≤ 11000
2.- 22* X₁₂ + 16* X₂₂ + 9*X₃₂ ≤ 2700
3.- 22*X₁₃ + 16* X₂₃ + 9*X₃₃ ≤ 3400
Demand constrain
Product huge
X₁₁ + X₁₂ + X₁₃ ≤ 710
Product average
X₂₁ + X₂₂ + X₂₃ ≤ 900
Product tiny
X₃₁ + X₃₂ + X₃₃ ≤ 350
Fraction SP/CC must be the same
First and second centers fraction SP/CC
(X₁₁ + X ₂₁ + X₃₁)/ 11000 = (X₁₂ + X₂₂ + X₃₂)/ 2700
2700*(X₁₁ + X ₂₁ + X₃₁) - 11000*(X₁₂ + X₂₂ + X₃₂) = 0
First and third centers fraction SP/CC
(X₁₁ + X ₂₁ + X₃₁)/ 11000 = ( X₁₃ + X₂₃ + X₃₃)/ 3400
3400*(X₁₁ + X ₂₁ + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0
The model is:
z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃
Subject to:
First center X₁₁ + X₂₁ + X₃₁ ≤ 550
Second center X₁₂ + X₂₂ + X₃₂ ≤ 750
Third center X₁₃ + X₂₃ + X₃₃ ≤ 275
22* X₁₁ + 16* X₂₁ + 9*X₃₁ ≤ 11000
22* X₁₂ + 16* X₂₂ + 9*X₃₂ ≤ 2700
22*X₁₃ + 16* X₂₃ + 9*X₃₃ ≤ 3400
X₁₁ + X₁₂ + X₁₃ ≤ 710
X₂₁ + X₂₂ + X₂₃ ≤ 900
X₃₁ + X₃₂ + X₃₃ ≤ 350
2700*(X₁₁ + X ₂₁ + X₃₁) - 11000*(X₁₂ + X₂₂ + X₃₂) = 0
3400*(X₁₁ + X ₂₁ + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0
Xij >= 0
