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Problem 2 (25 points): (Transportation problem) A car manufacturer has three assembly lines, Plant A, B, and C and three dist

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Answer #1

Let,

xij = number of cars transported from plant i to distributor j where i = {A=1,B=2,C=3} and j ={I=1,II=2,III=3}

Objective is to minimize transportation cost = Min 230x11+410x12+210x13+150x21+320x22+230x23+190x31+130x32+200x33

subject to,
Capacity constraints
x11+x12+x13 <= 200 (Plant A)
x21+x22+x23 <= 150 (Plant B)
x31+x32+x33 <= 250 (Plant C)

x11+x21+x31 = 120 (Distributor 1)
x12+x22+x32 = 270 (Distributor 2)
x13+x23+x33 = 200 (Distributor 3)

xij >= 0

Solving in solver we get following optimal transportation schedule

Plant A Plant B Plant C
Distributor 1 0 0 120
Distributor 2 200 70 0
Distributor 3 0 80 120

Minimized cost = 169600


Solver screenshot

2 A B C D E F G H I J K L 33 x12x13x21x22x23x31 0 2000 0 70 80 32 1200 120 Objective function 169600 1 200 150 5 Plant A 6 Pl

Solver formula

A B C D E F G H I J L M N x11 x12 x13 x21 22 23 x31 x32 x33 0 200 0 0 70 80 1200 120 Objective function =230*B3+410*C3+210*D3


Solver window

Solver Parameters X Set Objective: 5053 To: Max Min O Value of: 0 By Changing Variable Cells: $B$3:553 Subject to the Constra

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