Plant Production Capacity Fixed cost Variable cost per TV Let
1 10000 $9,000,000.00 $1600 X1 Number of TV manufactured in Plant 1
2 8000 $5,000,000.00 $2000 X2 Number of TV manufactured in Plant 2
3 9000 $3,000,000.00 $2300 X3 Number of TV manufactured in Plant 3
4 7000 $4,000,000.00 $2100 X4 Number of TV manufactured in Plant 4
5 6000 $1,000,000.00 $2400 X5 Number of TV manufactured in Plant 5
Y1 Binary Variable (1 if X1>0 else 0)
Y2 Binary Variable (1 if X2>0 else 0)
Y3 Binary Variable (1 if X3>0 else 0)
Y4 Binary Variable (1 if X4>0 else 0)
Y5 Binary Variable (1 if X5>0 else 0)
Objective Function
Profit= Number of TVs from each plant* Selling Price-Fixed Cost-Number of TVs from Each Plant * Variable cost in that plant location
Profit= (X1+X2+X3+X4+X5)*4000 -( 9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)-(X1*1600-X2*2000-X3*2300-X4*2100-X5*2400)
Profit= 4000X1+4000X2+4000X3+4000X4+4000X5-1600X1-2000X2-2300X3-2100X4-2400X5-(9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)
Z= 2400X1+2000X2+1700X3+1900X4+1600X5-(9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)
Subject to
Constraint 1
Maximum Sales can be 25000
X1+X2+X3+X4+X5=0
Binary Variables
Y1,Y2,Y3,Y4,Y5 are binary variables
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b)
Selling Capacity
X1 X2 X3 X4 X5
20000 0 8000 9000 0 3000
21000 0 8000 9000 0 4000
22000 9000 0 0 7000 6000
23000 10000 0 0 7000 6000
24000 10000 8000 0 0 6000
25000 10000 0 9000 0 6000
26000 9000 8000 9000 0 0
27000 10000 8000 9000 0 0
28000 10000 0 0 7000 6000
29000 0 8000 9000 6000 6000
30000 9000 8000 0 7000 6000
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